TSTP Solution File: LCL159-1 by EQP---0.9e
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : EQP---0.9e
% Problem : LCL159-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_eqp %s
% Computer : n027.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 : 600s
% DateTime : Sun Jul 17 09:41:23 EDT 2022
% Result : Unsatisfiable 0.71s 1.11s
% Output : Refutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of clauses : 83 ( 83 unt; 0 nHn; 15 RR)
% Number of literals : 83 ( 0 equ; 9 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 116 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,plain,
equal(implies(truth,A),A),
file('LCL159-1.p',unknown),
[] ).
cnf(2,plain,
equal(implies(implies(A,B),implies(implies(B,C),implies(A,C))),truth),
file('LCL159-1.p',unknown),
[] ).
cnf(3,plain,
equal(implies(implies(A,B),B),implies(implies(B,A),A)),
file('LCL159-1.p',unknown),
[] ).
cnf(4,plain,
equal(implies(implies(not(A),not(B)),implies(B,A)),truth),
file('LCL159-1.p',unknown),
[] ).
cnf(5,plain,
equal(or(A,B),implies(not(A),B)),
file('LCL159-1.p',unknown),
[] ).
cnf(6,plain,
equal(implies(not(A),B),or(A,B)),
inference(flip,[status(thm),theory(equality)],[5]),
[iquote('flip(5)')] ).
cnf(8,plain,
equal(or(A,B),or(B,A)),
file('LCL159-1.p',unknown),
[] ).
cnf(9,plain,
equal(not(or(not(A),not(B))),and(A,B)),
inference(flip,[status(thm),theory(equality)],[1]),
[iquote('flip(1)')] ).
cnf(10,plain,
equal(and(and(A,B),C),and(A,and(B,C))),
file('LCL159-1.p',unknown),
[] ).
cnf(11,plain,
equal(and(A,B),and(B,A)),
file('LCL159-1.p',unknown),
[] ).
cnf(12,plain,
equal(xor(A,B),or(and(A,not(B)),and(not(A),B))),
file('LCL159-1.p',unknown),
[] ).
cnf(13,plain,
equal(or(and(A,not(B)),and(not(A),B)),xor(A,B)),
inference(flip,[status(thm),theory(equality)],[12]),
[iquote('flip(12)')] ).
cnf(16,plain,
equal(not(truth),falsehood),
file('LCL159-1.p',unknown),
[] ).
cnf(17,plain,
~ equal(xor(xor(x,truth),y),xor(x,xor(truth,y))),
inference(flip,[status(thm),theory(equality)],[1]),
[iquote('flip(1)')] ).
cnf(18,plain,
equal(implies(A,implies(implies(A,B),B)),truth),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1,2]),1]),
[iquote('para(1,2),demod([1])')] ).
cnf(25,plain,
equal(or(truth,A),implies(falsehood,A)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[16,6]),1]),
[iquote('para(16,6),flip(1)')] ).
cnf(32,plain,
equal(implies(implies(not(A),falsehood),A),truth),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1,4]),16]),
[iquote('para(1,4),demod([16])')] ).
cnf(41,plain,
equal(or(A,truth),implies(falsehood,A)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[25,8]),1]),
[iquote('para(25,8),flip(1)')] ).
cnf(43,plain,
equal(implies(A,A),truth),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1,18]),1]),
[iquote('para(1,18),demod([1])')] ).
cnf(52,plain,
equal(or(A,not(A)),truth),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[43,6]),1]),
[iquote('para(43,6),flip(1)')] ).
cnf(53,plain,
equal(or(not(A),A),truth),
inference(para,[status(thm),theory(equality)],[8,52]),
[iquote('para(8,52)')] ).
cnf(57,plain,
equal(implies(not(not(A)),A),truth),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[53,5]),1]),
[iquote('para(53,5),flip(1)')] ).
cnf(58,plain,
equal(or(A,B),implies(not(B),A)),
inference(para,[status(thm),theory(equality)],[8,5]),
[iquote('para(8,5)')] ).
cnf(59,plain,
equal(implies(not(A),B),or(B,A)),
inference(flip,[status(thm),theory(equality)],[58]),
[iquote('flip(58)')] ).
cnf(63,plain,
equal(not(or(falsehood,not(A))),and(truth,A)),
inference(para,[status(thm),theory(equality)],[16,9]),
[iquote('para(16,9)')] ).
cnf(65,plain,
equal(not(or(falsehood,falsehood)),and(truth,truth)),
inference(para,[status(thm),theory(equality)],[16,63]),
[iquote('para(16,63)')] ).
cnf(68,plain,
equal(not(implies(not(not(A)),not(B))),and(A,B)),
inference(para,[status(thm),theory(equality)],[5,9]),
[iquote('para(5,9)')] ).
cnf(70,plain,
equal(implies(not(A),truth),implies(falsehood,A)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[41,5]),1]),
[iquote('para(41,5),flip(1)')] ).
cnf(71,plain,
equal(not(or(and(A,B),not(C))),and(or(not(A),not(B)),C)),
inference(para,[status(thm),theory(equality)],[9,9]),
[iquote('para(9,9)')] ).
cnf(72,plain,
equal(not(or(not(A),and(B,C))),and(A,or(not(B),not(C)))),
inference(para,[status(thm),theory(equality)],[9,9]),
[iquote('para(9,9)')] ).
cnf(74,plain,
equal(not(falsehood),truth),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[57,32]),1]),
[iquote('para(57,32),demod([1])')] ).
cnf(75,plain,
equal(or(falsehood,A),A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[74,6]),1]),1]),
[iquote('para(74,6),demod([1]),flip(1)')] ).
cnf(76,plain,
equal(and(truth,truth),truth),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[65]),75,74]),1]),
[iquote('back_demod(65),demod([75,74]),flip(1)')] ).
cnf(77,plain,
equal(not(not(A)),and(truth,A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[63]),75]),
[iquote('back_demod(63),demod([75])')] ).
cnf(78,plain,
equal(not(implies(and(truth,A),not(B))),and(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[68]),77]),
[iquote('back_demod(68),demod([77])')] ).
cnf(79,plain,
equal(implies(and(truth,A),A),truth),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[57]),77]),
[iquote('back_demod(57),demod([77])')] ).
cnf(85,plain,
equal(and(truth,falsehood),falsehood),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[74,77]),16]),1]),
[iquote('para(74,77),demod([16]),flip(1)')] ).
cnf(88,plain,
equal(implies(not(and(A,not(B))),and(not(A),B)),xor(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[13,5]),1]),
[iquote('para(13,5),flip(1)')] ).
cnf(101,plain,
equal(or(and(A,not(B)),and(B,not(A))),xor(A,B)),
inference(para,[status(thm),theory(equality)],[11,13]),
[iquote('para(11,13)')] ).
cnf(102,plain,
equal(xor(A,B),or(and(A,not(B)),and(B,not(A)))),
inference(flip,[status(thm),theory(equality)],[101]),
[iquote('flip(101)')] ).
cnf(103,plain,
equal(implies(not(A),falsehood),A),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[75,58]),1]),
[iquote('para(75,58),flip(1)')] ).
cnf(104,plain,
equal(not(A),implies(and(truth,A),falsehood)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[77,103]),1]),
[iquote('para(77,103),flip(1)')] ).
cnf(105,plain,
equal(implies(implies(and(truth,A),falsehood),falsehood),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[103]),104]),
[iquote('back_demod(103),demod([104])')] ).
cnf(106,plain,
equal(xor(A,B),or(and(A,implies(and(truth,B),falsehood)),and(B,implies(and(truth,A),falsehood)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[102]),104,104]),
[iquote('back_demod(102),demod([104,104])')] ).
cnf(114,plain,
equal(or(and(A,implies(and(truth,B),falsehood)),and(B,implies(and(truth,A),falsehood))),implies(implies(and(truth,and(A,implies(and(truth,B),falsehood))),falsehood),and(implies(and(truth,A),falsehood),B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[88]),104,104,104,106]),1]),
[iquote('back_demod(88),demod([104,104,104,106]),flip(1)')] ).
cnf(119,plain,
equal(xor(A,B),implies(implies(and(truth,and(A,implies(and(truth,B),falsehood))),falsehood),and(implies(and(truth,A),falsehood),B))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[106]),114]),
[iquote('back_demod(106),demod([114])')] ).
cnf(120,plain,
~ equal(implies(implies(and(truth,and(x,implies(and(truth,implies(implies(and(truth,and(truth,implies(and(truth,y),falsehood))),falsehood),and(falsehood,y))),falsehood))),falsehood),and(implies(and(truth,x),falsehood),implies(implies(and(truth,and(truth,implies(and(truth,y),falsehood))),falsehood),and(falsehood,y)))),implies(implies(and(truth,and(implies(implies(and(truth,and(x,falsehood)),falsehood),and(implies(and(truth,x),falsehood),truth)),implies(and(truth,y),falsehood))),falsehood),and(implies(and(truth,implies(implies(and(truth,and(x,falsehood)),falsehood),and(implies(and(truth,x),falsehood),truth))),falsehood),y))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[17]),119,76,1,119,119,76,1,119]),1]),
[iquote('back_demod(17),demod([119,76,1,119,119,76,1,119]),flip(1)')] ).
cnf(124,plain,
equal(implies(and(truth,implies(and(truth,A),implies(and(truth,B),falsehood))),falsehood),and(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[78]),104,104]),
[iquote('back_demod(78),demod([104,104])')] ).
cnf(125,plain,
equal(implies(and(truth,implies(and(truth,A),falsehood)),falsehood),and(truth,A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[77]),104,104]),
[iquote('back_demod(77),demod([104,104])')] ).
cnf(126,plain,
equal(implies(and(truth,or(implies(and(truth,A),falsehood),and(B,C))),falsehood),and(A,or(implies(and(truth,B),falsehood),implies(and(truth,C),falsehood)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[72]),104,104,104,104]),
[iquote('back_demod(72),demod([104,104,104,104])')] ).
cnf(127,plain,
equal(and(A,or(implies(and(truth,B),falsehood),implies(and(truth,C),falsehood))),implies(and(truth,or(implies(and(truth,A),falsehood),and(B,C))),falsehood)),
inference(flip,[status(thm),theory(equality)],[126]),
[iquote('flip(126)')] ).
cnf(128,plain,
equal(implies(and(truth,or(and(A,B),implies(and(truth,C),falsehood))),falsehood),and(or(implies(and(truth,A),falsehood),implies(and(truth,B),falsehood)),C)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[71]),104,104,104,104]),
[iquote('back_demod(71),demod([104,104,104,104])')] ).
cnf(129,plain,
equal(and(or(implies(and(truth,A),falsehood),implies(and(truth,B),falsehood)),C),implies(and(truth,or(and(A,B),implies(and(truth,C),falsehood))),falsehood)),
inference(flip,[status(thm),theory(equality)],[128]),
[iquote('flip(128)')] ).
cnf(130,plain,
equal(implies(implies(and(truth,A),falsehood),truth),implies(falsehood,A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[70]),104]),
[iquote('back_demod(70),demod([104])')] ).
cnf(134,plain,
equal(or(A,B),implies(implies(and(truth,B),falsehood),A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[59]),104]),1]),
[iquote('back_demod(59),demod([104]),flip(1)')] ).
cnf(139,plain,
equal(implies(and(truth,implies(and(truth,A),and(B,C))),falsehood),and(implies(and(truth,C),implies(and(truth,B),falsehood)),A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[129]),134,125,134,125]),1]),
[iquote('back_demod(129),demod([134,125,134,125]),flip(1)')] ).
cnf(140,plain,
equal(implies(and(truth,implies(implies(and(truth,and(A,B)),falsehood),implies(and(truth,C),falsehood))),falsehood),and(C,implies(and(truth,B),implies(and(truth,A),falsehood)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[127]),134,125,134]),1]),
[iquote('back_demod(127),demod([134,125,134]),flip(1)')] ).
cnf(161,plain,
equal(implies(implies(and(truth,A),falsehood),B),implies(implies(and(truth,B),falsehood),A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[8]),134,134]),
[iquote('back_demod(8),demod([134,134])')] ).
cnf(181,plain,
equal(implies(A,implies(implies(B,A),A)),truth),
inference(para,[status(thm),theory(equality)],[3,18]),
[iquote('para(3,18)')] ).
cnf(182,plain,
equal(implies(A,truth),truth),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1,181]),43]),
[iquote('para(1,181),demod([43])')] ).
cnf(183,plain,
equal(implies(falsehood,A),truth),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[130]),182]),1]),
[iquote('back_demod(130),demod([182]),flip(1)')] ).
cnf(206,plain,
equal(implies(implies(and(A,truth),falsehood),falsehood),A),
inference(para,[status(thm),theory(equality)],[11,105]),
[iquote('para(11,105)')] ).
cnf(215,plain,
equal(and(truth,and(truth,A)),and(truth,A)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[76,10]),1]),
[iquote('para(76,10),flip(1)')] ).
cnf(216,plain,
~ equal(implies(implies(and(truth,and(implies(implies(and(truth,and(x,falsehood)),falsehood),and(implies(and(truth,x),falsehood),truth)),implies(and(truth,y),falsehood))),falsehood),and(implies(and(truth,implies(implies(and(truth,and(x,falsehood)),falsehood),and(implies(and(truth,x),falsehood),truth))),falsehood),y)),implies(implies(and(truth,and(x,and(truth,y))),falsehood),and(implies(and(truth,x),falsehood),implies(and(truth,y),and(falsehood,y))))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[120]),215,125,139,85,43,182,215,125]),1]),
[iquote('back_demod(120),demod([215,125,139,85,43,182,215,125]),flip(1)')] ).
cnf(229,plain,
equal(and(truth,and(falsehood,A)),and(falsehood,A)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[85,10]),1]),
[iquote('para(85,10),flip(1)')] ).
cnf(232,plain,
equal(and(truth,and(A,falsehood)),and(falsehood,A)),
inference(para,[status(thm),theory(equality)],[11,229]),
[iquote('para(11,229)')] ).
cnf(233,plain,
~ equal(implies(implies(and(truth,and(implies(implies(and(falsehood,x),falsehood),and(implies(and(truth,x),falsehood),truth)),implies(and(truth,y),falsehood))),falsehood),and(implies(and(truth,implies(implies(and(falsehood,x),falsehood),and(implies(and(truth,x),falsehood),truth))),falsehood),y)),implies(implies(and(truth,and(x,and(truth,y))),falsehood),and(implies(and(truth,x),falsehood),implies(and(truth,y),and(falsehood,y))))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[216]),232,232]),
[iquote('back_demod(216),demod([232,232])')] ).
cnf(248,plain,
equal(implies(and(falsehood,A),and(A,falsehood)),truth),
inference(para,[status(thm),theory(equality)],[232,79]),
[iquote('para(232,79)')] ).
cnf(294,plain,
equal(implies(implies(A,falsehood),falsehood),A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[183,3]),1]),1]),
[iquote('para(183,3),demod([1]),flip(1)')] ).
cnf(295,plain,
equal(and(A,truth),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[206]),294]),
[iquote('back_demod(206),demod([294])')] ).
cnf(296,plain,
~ equal(implies(implies(and(truth,and(implies(implies(and(falsehood,x),falsehood),implies(and(truth,x),falsehood)),implies(and(truth,y),falsehood))),falsehood),and(implies(and(truth,implies(implies(and(falsehood,x),falsehood),implies(and(truth,x),falsehood))),falsehood),y)),implies(implies(and(truth,and(x,and(truth,y))),falsehood),and(implies(and(truth,x),falsehood),implies(and(truth,y),and(falsehood,y))))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[233]),295,295]),
[iquote('back_demod(233),demod([295,295])')] ).
cnf(297,plain,
equal(and(truth,A),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[105]),294]),
[iquote('back_demod(105),demod([294])')] ).
cnf(298,plain,
~ equal(implies(implies(and(implies(implies(and(falsehood,x),falsehood),implies(x,falsehood)),implies(y,falsehood)),falsehood),and(implies(implies(implies(and(falsehood,x),falsehood),implies(x,falsehood)),falsehood),y)),implies(implies(and(x,y),falsehood),and(implies(x,falsehood),implies(y,and(falsehood,y))))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[296]),297,297,297,297,297,297,297,297,297]),
[iquote('back_demod(296),demod([297,297,297,297,297,297,297,297,297])')] ).
cnf(310,plain,
equal(implies(implies(A,falsehood),B),implies(implies(B,falsehood),A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[161]),297,297]),
[iquote('back_demod(161),demod([297,297])')] ).
cnf(322,plain,
equal(implies(implies(implies(and(A,B),falsehood),implies(C,falsehood)),falsehood),and(C,implies(B,implies(A,falsehood)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[140]),297,297,297,297,297]),
[iquote('back_demod(140),demod([297,297,297,297,297])')] ).
cnf(323,plain,
~ equal(implies(implies(and(implies(implies(and(falsehood,x),falsehood),implies(x,falsehood)),implies(y,falsehood)),falsehood),and(x,y)),implies(implies(and(x,y),falsehood),and(implies(x,falsehood),implies(y,and(falsehood,y))))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[298]),322,43,182,295]),
[iquote('back_demod(298),demod([322,43,182,295])')] ).
cnf(328,plain,
equal(implies(implies(A,implies(B,falsehood)),falsehood),and(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[124]),297,297,297]),
[iquote('back_demod(124),demod([297,297,297])')] ).
cnf(337,plain,
equal(and(A,falsehood),falsehood),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[43,328]),182,1]),1]),
[iquote('para(43,328),demod([182,1]),flip(1)')] ).
cnf(338,plain,
equal(implies(and(falsehood,A),falsehood),truth),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[248]),337]),
[iquote('back_demod(248),demod([337])')] ).
cnf(339,plain,
~ equal(implies(implies(and(implies(x,falsehood),implies(y,falsehood)),falsehood),and(x,y)),implies(implies(and(x,y),falsehood),and(implies(x,falsehood),implies(y,and(falsehood,y))))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[323]),338,1]),
[iquote('back_demod(323),demod([338,1])')] ).
cnf(343,plain,
equal(and(falsehood,A),falsehood),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[337,11]),1]),
[iquote('para(337,11),flip(1)')] ).
cnf(344,plain,
~ equal(implies(implies(and(implies(x,falsehood),implies(y,falsehood)),falsehood),and(x,y)),implies(implies(and(x,y),falsehood),and(implies(x,falsehood),implies(y,falsehood)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[339]),343]),
[iquote('back_demod(339),demod([343])')] ).
cnf(345,plain,
$false,
inference(conflict,[status(thm)],[344,310]),
[iquote('conflict(344,310)')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL159-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_eqp %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 2 10:30:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.71/1.11 ----- EQP 0.9e, May 2009 -----
% 0.71/1.11 The job began on n027.cluster.edu, Sat Jul 2 10:30:39 2022
% 0.71/1.11 The command was "./eqp09e".
% 0.71/1.11
% 0.71/1.11 set(prolog_style_variables).
% 0.71/1.11 set(lrpo).
% 0.71/1.11 set(basic_paramod).
% 0.71/1.11 set(functional_subsume).
% 0.71/1.11 set(ordered_paramod).
% 0.71/1.11 set(prime_paramod).
% 0.71/1.11 set(para_pairs).
% 0.71/1.11 assign(pick_given_ratio,4).
% 0.71/1.11 clear(print_kept).
% 0.71/1.11 clear(print_new_demod).
% 0.71/1.11 clear(print_back_demod).
% 0.71/1.11 clear(print_given).
% 0.71/1.11 assign(max_mem,64000).
% 0.71/1.11 end_of_commands.
% 0.71/1.11
% 0.71/1.11 Usable:
% 0.71/1.11 end_of_list.
% 0.71/1.11
% 0.71/1.11 Sos:
% 0.71/1.11 0 (wt=-1) [] implies(truth,A) = A.
% 0.71/1.11 0 (wt=-1) [] implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth.
% 0.71/1.11 0 (wt=-1) [] implies(implies(A,B),B) = implies(implies(B,A),A).
% 0.71/1.11 0 (wt=-1) [] implies(implies(not(A),not(B)),implies(B,A)) = truth.
% 0.71/1.11 0 (wt=-1) [] or(A,B) = implies(not(A),B).
% 0.71/1.11 0 (wt=-1) [] or(or(A,B),C) = or(A,or(B,C)).
% 0.71/1.11 0 (wt=-1) [] or(A,B) = or(B,A).
% 0.71/1.11 0 (wt=-1) [] and(A,B) = not(or(not(A),not(B))).
% 0.71/1.11 0 (wt=-1) [] and(and(A,B),C) = and(A,and(B,C)).
% 0.71/1.11 0 (wt=-1) [] and(A,B) = and(B,A).
% 0.71/1.11 0 (wt=-1) [] xor(A,B) = or(and(A,not(B)),and(not(A),B)).
% 0.71/1.11 0 (wt=-1) [] xor(A,B) = xor(B,A).
% 0.71/1.11 0 (wt=-1) [] and_star(A,B) = not(or(not(A),not(B))).
% 0.71/1.11 0 (wt=-1) [] and_star(and_star(A,B),C) = and_star(A,and_star(B,C)).
% 0.71/1.11 0 (wt=-1) [] and_star(A,B) = and_star(B,A).
% 0.71/1.11 0 (wt=-1) [] not(truth) = falsehood.
% 0.71/1.11 0 (wt=-1) [] -(xor(x,xor(truth,y)) = xor(xor(x,truth),y)).
% 0.71/1.11 end_of_list.
% 0.71/1.11
% 0.71/1.11 Demodulators:
% 0.71/1.11 end_of_list.
% 0.71/1.11
% 0.71/1.11 Passive:
% 0.71/1.11 end_of_list.
% 0.71/1.11
% 0.71/1.11 Starting to process input.
% 0.71/1.11
% 0.71/1.11 ** KEPT: 1 (wt=5) [] implies(truth,A) = A.
% 0.71/1.11 1 is a new demodulator.
% 0.71/1.11
% 0.71/1.11 ** KEPT: 2 (wt=13) [] implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth.
% 0.71/1.11 2 is a new demodulator.
% 0.71/1.11
% 0.71/1.11 ** KEPT: 3 (wt=11) [] implies(implies(A,B),B) = implies(implies(B,A),A).
% 0.71/1.11 clause forward subsumed: 0 (wt=11) [flip(3)] implies(implies(B,A),A) = implies(implies(A,B),B).
% 0.71/1.11
% 0.71/1.11 ** KEPT: 4 (wt=11) [] implies(implies(not(A),not(B)),implies(B,A)) = truth.
% 0.71/1.11 4 is a new demodulator.
% 0.71/1.11
% 0.71/1.11 ** KEPT: 5 (wt=8) [] or(A,B) = implies(not(A),B).
% 0.71/1.11
% 0.71/1.11 ** KEPT: 6 (wt=8) [flip(5)] implies(not(A),B) = or(A,B).
% 0.71/1.11 clause forward subsumed: 0 (wt=8) [flip(6)] or(A,B) = implies(not(A),B).
% 0.71/1.11
% 0.71/1.11 ** KEPT: 7 (wt=11) [] or(or(A,B),C) = or(A,or(B,C)).
% 0.71/1.11 7 is a new demodulator.
% 0.71/1.11
% 0.71/1.11 ** KEPT: 8 (wt=7) [] or(A,B) = or(B,A).
% 0.71/1.11 clause forward subsumed: 0 (wt=7) [flip(8)] or(B,A) = or(A,B).
% 0.71/1.11
% 0.71/1.11 ** KEPT: 9 (wt=10) [flip(1)] not(or(not(A),not(B))) = and(A,B).
% 0.71/1.11 9 is a new demodulator.
% 0.71/1.11
% 0.71/1.11 ** KEPT: 10 (wt=11) [] and(and(A,B),C) = and(A,and(B,C)).
% 0.71/1.11 10 is a new demodulator.
% 0.71/1.11
% 0.71/1.11 ** KEPT: 11 (wt=7) [] and(A,B) = and(B,A).
% 0.71/1.11 clause forward subsumed: 0 (wt=7) [flip(11)] and(B,A) = and(A,B).
% 0.71/1.11
% 0.71/1.11 ** KEPT: 12 (wt=13) [] xor(A,B) = or(and(A,not(B)),and(not(A),B)).
% 0.71/1.11
% 0.71/1.11 ** KEPT: 13 (wt=13) [flip(12)] or(and(A,not(B)),and(not(A),B)) = xor(A,B).
% 0.71/1.11 clause forward subsumed: 0 (wt=13) [flip(13)] xor(A,B) = or(and(A,not(B)),and(not(A),B)).
% 0.71/1.11
% 0.71/1.11 ** KEPT: 14 (wt=7) [] xor(A,B) = xor(B,A).
% 0.71/1.11 clause forward subsumed: 0 (wt=7) [flip(14)] xor(B,A) = xor(A,B).
% 0.71/1.11
% 0.71/1.11 ** KEPT: 15 (wt=7) [demod([9])] and_star(A,B) = and(A,B).
% 0.71/1.11 15 is a new demodulator.
% 0.71/1.11 clause forward subsumed: 0 (wt=11) [demod([15,15,10,15,15])] and(A,and(B,C)) = and(A,and(B,C)).
% 0.71/1.11 clause forward subsumed: 0 (wt=7) [demod([15,15])] and(A,B) = and(B,A).
% 0.71/1.11
% 0.71/1.11 ** KEPT: 16 (wt=4) [] not(truth) = falsehood.
% 0.71/1.11 16 is a new demodulator.
% 0.71/1.11
% 0.71/1.11 ** KEPT: 17 (wt=11) [flip(1)] -(xor(xor(x,truth),y) = xor(x,xor(truth,y))).
% 0.71/1.11 ---------------- PROOF FOUND ----------------
% 0.71/1.11 % SZS status Unsatisfiable
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 After processing input:
% 0.71/1.11
% 0.71/1.11 Usable:
% 0.71/1.11 end_of_list.
% 0.71/1.11
% 0.71/1.11 Sos:
% 0.71/1.11 16 (wt=4) [] not(truth) = falsehood.
% 0.71/1.11 1 (wt=5) [] implies(truth,A) = A.
% 0.71/1.11 8 (wt=7) [] or(A,B) = or(B,A).
% 0.71/1.11 11 (wt=7) [] and(A,B) = and(B,A).
% 0.71/1.11 14 (wt=7) [] xor(A,B) = xor(B,A).
% 0.71/1.11 15 (wt=7) [demod([9])] and_star(A,B) = and(A,B).
% 0.71/1.11 5 (wt=8) [] or(A,B) = implies(not(A),B).
% 0.71/1.11 6 (wt=8) [flip(5)] implies(not(A),B) = or(A,B).
% 0.71/1.11 9 (wt=10) [flip(1)] not(or(not(A),not(B))) = and(A,B).
% 0.71/1.11 3 (wt=11) [] implies(implies(A,B),B) = implies(implies(B,A),A).
% 0.71/1.11 4 (wt=11) [] implies(implies(not(A),not(B)),implies(B,A)) = truth.
% 0.71/1.11 7 (wt=11) [] or(or(A,B),C) = or(A,or(B,C)).
% 0.71/1.11 10 (wt=11) [] and(and(A,B),C) = and(A,and(B,C)).
% 0.71/1.11 17 (wt=11) [flip(1)] -(xor(xor(x,truth),y) = xor(x,xor(truth,y))).
% 0.71/1.11 2 (wt=13) [] implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth.
% 0.71/1.11 12 (wt=13) [] xor(A,B) = or(and(A,not(B)),and(not(A),B)).
% 0.71/1.11 13 (wt=13) [flip(12)] or(and(A,not(B)),and(not(A),B)) = xor(A,B).
% 0.71/1.11 end_of_list.
% 0.71/1.11
% 0.71/1.11 Demodulators:
% 0.71/1.11 1 (wt=5) [] implies(truth,A) = A.
% 0.71/1.11 2 (wt=13) [] implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth.
% 0.71/1.11 4 (wt=11) [] implies(implies(not(A),not(B)),implies(B,A)) = truth.
% 0.71/1.11 7 (wt=11) [] or(or(A,B),C) = or(A,or(B,C)).
% 0.71/1.11 9 (wt=10) [flip(1)] not(or(not(A),not(B))) = and(A,B).
% 0.71/1.11 10 (wt=11) [] and(and(A,B),C) = and(A,and(B,C)).
% 0.71/1.11 15 (wt=7) [demod([9])] and_star(A,B) = and(A,B).
% 0.71/1.11 16 (wt=4) [] not(truth) = falsehood.
% 0.71/1.11 end_of_list.
% 0.71/1.11
% 0.71/1.11 Passive:
% 0.71/1.11 end_of_list.
% 0.71/1.11
% 0.71/1.11 UNIT CONFLICT from 344 and 310 at 0.02 seconds.
% 0.71/1.11
% 0.71/1.11 ---------------- PROOF ----------------
% 0.71/1.11 % SZS output start Refutation
% See solution above
% 0.71/1.11 ------------ end of proof -------------
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 ------------- memory usage ------------
% 0.71/1.11 Memory dynamically allocated (tp_alloc): 976.
% 0.71/1.11 type (bytes each) gets frees in use avail bytes
% 0.71/1.11 sym_ent ( 96) 61 0 61 0 5.7 K
% 0.71/1.11 term ( 16) 28767 21718 7049 99 138.3 K
% 0.71/1.11 gen_ptr ( 8) 40653 8675 31978 82 250.5 K
% 0.71/1.11 context ( 808) 21503 21501 2 3 3.9 K
% 0.71/1.11 trail ( 12) 2178 2178 0 6 0.1 K
% 0.71/1.11 bt_node ( 68) 6527 6524 3 14 1.1 K
% 0.71/1.11 ac_position (285432) 0 0 0 0 0.0 K
% 0.71/1.11 ac_match_pos (14044) 0 0 0 0 0.0 K
% 0.71/1.11 ac_match_free_vars_pos (4020)
% 0.71/1.11 0 0 0 0 0.0 K
% 0.71/1.11 discrim ( 12) 7004 3249 3755 461 49.4 K
% 0.71/1.11 flat ( 40) 54361 54361 0 59 2.3 K
% 0.71/1.11 discrim_pos ( 12) 1480 1480 0 1 0.0 K
% 0.71/1.11 fpa_head ( 12) 2598 0 2598 0 30.4 K
% 0.71/1.11 fpa_tree ( 28) 2070 2070 0 69 1.9 K
% 0.71/1.11 fpa_pos ( 36) 593 593 0 1 0.0 K
% 0.71/1.11 literal ( 12) 1362 1018 344 0 4.0 K
% 0.71/1.11 clause ( 24) 1362 1018 344 0 8.1 K
% 0.71/1.11 list ( 12) 308 251 57 4 0.7 K
% 0.71/1.11 list_pos ( 20) 1699 898 801 15 15.9 K
% 0.71/1.11 pair_index ( 40) 2 0 2 0 0.1 K
% 0.71/1.11
% 0.71/1.11 -------------- statistics -------------
% 0.71/1.11 Clauses input 17
% 0.71/1.11 Usable input 0
% 0.71/1.11 Sos input 17
% 0.71/1.11 Demodulators input 0
% 0.71/1.11 Passive input 0
% 0.71/1.11
% 0.71/1.11 Processed BS (before search) 25
% 0.71/1.11 Forward subsumed BS 8
% 0.71/1.11 Kept BS 17
% 0.71/1.11 New demodulators BS 8
% 0.71/1.11 Back demodulated BS 0
% 0.71/1.11
% 0.71/1.11 Clauses or pairs given 976
% 0.71/1.11 Clauses generated 883
% 0.71/1.11 Forward subsumed 556
% 0.71/1.11 Deleted by weight 0
% 0.71/1.11 Deleted by variable count 0
% 0.71/1.11 Kept 327
% 0.71/1.11 New demodulators 241
% 0.71/1.11 Back demodulated 182
% 0.71/1.11 Ordered paramod prunes 0
% 0.71/1.11 Basic paramod prunes 1205
% 0.71/1.11 Prime paramod prunes 47
% 0.71/1.11 Semantic prunes 0
% 0.71/1.11
% 0.71/1.11 Rewrite attmepts 11894
% 0.71/1.11 Rewrites 1332
% 0.71/1.11
% 0.71/1.11 FPA overloads 0
% 0.71/1.11 FPA underloads 0
% 0.71/1.11
% 0.71/1.11 Usable size 0
% 0.71/1.11 Sos size 161
% 0.71/1.11 Demodulators size 135
% 0.71/1.11 Passive size 0
% 0.71/1.11 Disabled size 182
% 0.71/1.11
% 0.71/1.11 Proofs found 1
% 0.71/1.11
% 0.71/1.11 ----------- times (seconds) ----------- Sat Jul 2 10:30:39 2022
% 0.71/1.11
% 0.71/1.11 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 0.71/1.11 system CPU time 0.03 (0 hr, 0 min, 0 sec)
% 0.71/1.11 wall-clock time 0 (0 hr, 0 min, 0 sec)
% 0.71/1.11 input time 0.00
% 0.71/1.11 paramodulation time 0.00
% 0.71/1.11 demodulation time 0.00
% 0.71/1.11 orient time 0.00
% 0.71/1.11 weigh time 0.00
% 0.71/1.11 forward subsume time 0.00
% 0.71/1.11 back demod find time 0.00
% 0.71/1.11 conflict time 0.00
% 0.71/1.11 LRPO time 0.00
% 0.71/1.11 store clause time 0.00
% 0.71/1.11 disable clause time 0.00
% 0.71/1.11 prime paramod time 0.00
% 0.71/1.11 semantics time 0.00
% 0.71/1.11
% 0.71/1.11 EQP interrupted
%------------------------------------------------------------------------------