%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM487+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 13:08:33 EDT 2022
% Result : Theorem 15.34s 15.56s
% Output : Refutation 15.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 27
% Syntax : Number of clauses : 66 ( 36 unt; 2 nHn; 65 RR)
% Number of literals : 143 ( 58 equ; 78 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
sz10 != sz00,
file('NUM487+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| aNaturalNumber0(sdtpldt0(A,B)) ),
file('NUM487+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| sdtpldt0(A,B) = sdtpldt0(B,A) ),
file('NUM487+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ aNaturalNumber0(A)
| sdtpldt0(A,sz00) = A ),
file('NUM487+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ aNaturalNumber0(A)
| A = sdtpldt0(sz00,A) ),
file('NUM487+1.p',unknown),
[] ).
cnf(8,plain,
( ~ aNaturalNumber0(A)
| sdtpldt0(sz00,A) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.2')] ).
cnf(11,axiom,
( ~ aNaturalNumber0(A)
| sdtasdt0(A,sz10) = A ),
file('NUM487+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ aNaturalNumber0(A)
| A = sdtasdt0(sz10,A) ),
file('NUM487+1.p',unknown),
[] ).
cnf(13,plain,
( ~ aNaturalNumber0(A)
| sdtasdt0(sz10,A) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[12])]),
[iquote('copy,12,flip.2')] ).
cnf(17,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(C)
| sdtasdt0(A,sdtpldt0(B,C)) = sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) ),
file('NUM487+1.p',unknown),
[] ).
cnf(18,plain,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(C)
| sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) = sdtasdt0(A,sdtpldt0(B,C)) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[17])]),
[iquote('copy,17,flip.4')] ).
cnf(19,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(C)
| sdtasdt0(sdtpldt0(B,C),A) = sdtpldt0(sdtasdt0(B,A),sdtasdt0(C,A)) ),
file('NUM487+1.p',unknown),
[] ).
cnf(20,plain,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(C)
| sdtpldt0(sdtasdt0(B,A),sdtasdt0(C,A)) = sdtasdt0(sdtpldt0(B,C),A) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[19])]),
[iquote('copy,19,flip.4')] ).
cnf(22,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(C)
| sdtpldt0(B,A) != sdtpldt0(C,A)
| B = C ),
file('NUM487+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| sdtpldt0(A,B) != sz00
| A = sz00 ),
file('NUM487+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| sdtlse_qdt0(A,B)
| ~ aNaturalNumber0(C)
| sdtpldt0(A,C) != B ),
file('NUM487+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| ~ sdtlse_qdt0(A,B)
| C != sdtmndt0(B,A)
| aNaturalNumber0(C) ),
file('NUM487+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| ~ sdtlse_qdt0(A,B)
| C != sdtmndt0(B,A)
| sdtpldt0(A,C) = B ),
file('NUM487+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| ~ sdtlse_qdt0(A,B)
| C = sdtmndt0(B,A)
| ~ aNaturalNumber0(C)
| sdtpldt0(A,C) != B ),
file('NUM487+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| sdtlse_qdt0(A,B)
| sdtlse_qdt0(B,A) ),
file('NUM487+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| doDivides0(A,B)
| ~ aNaturalNumber0(C)
| B != sdtasdt0(A,C) ),
file('NUM487+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ aNaturalNumber0(A)
| ~ isPrime0(A)
| ~ aNaturalNumber0(B)
| ~ doDivides0(B,A)
| B = sz10
| B = A ),
file('NUM487+1.p',unknown),
[] ).
cnf(71,axiom,
( xr = xn
| ~ sdtlse_qdt0(xr,xn) ),
file('NUM487+1.p',unknown),
[] ).
cnf(72,plain,
( ~ aNaturalNumber0(A)
| aNaturalNumber0(sdtpldt0(A,A)) ),
inference(factor,[status(thm)],[2]),
[iquote('factor,2.1.2')] ).
cnf(84,plain,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,B)) = sdtasdt0(A,sdtpldt0(B,B)) ),
inference(factor,[status(thm)],[18]),
[iquote('factor,18.2.3')] ).
cnf(87,plain,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| sdtpldt0(sdtasdt0(B,A),sdtasdt0(B,A)) = sdtasdt0(sdtpldt0(B,B),A) ),
inference(factor,[status(thm)],[20]),
[iquote('factor,20.2.3')] ).
cnf(92,plain,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| sdtpldt0(B,A) != sdtpldt0(A,A)
| B = A ),
inference(factor,[status(thm)],[22]),
[iquote('factor,22.1.3')] ).
cnf(102,plain,
( ~ aNaturalNumber0(A)
| sdtpldt0(A,A) != sz00
| A = sz00 ),
inference(factor,[status(thm)],[25]),
[iquote('factor,25.1.2')] ).
cnf(110,plain,
( ~ aNaturalNumber0(A)
| ~ sdtlse_qdt0(A,A)
| B = sdtmndt0(A,A)
| ~ aNaturalNumber0(B)
| sdtpldt0(A,B) != A ),
inference(factor,[status(thm)],[33]),
[iquote('factor,33.1.2')] ).
cnf(129,plain,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| doDivides0(A,B)
| sdtasdt0(A,B) != B ),
inference(flip,[status(thm),theory(equality)],[inference(factor,[status(thm)],[50])]),
[iquote('factor,50.2.4,flip.4')] ).
cnf(163,axiom,
A = A,
file('NUM487+1.p',unknown),
[] ).
cnf(164,axiom,
aNaturalNumber0(sz00),
file('NUM487+1.p',unknown),
[] ).
cnf(165,axiom,
aNaturalNumber0(sz10),
file('NUM487+1.p',unknown),
[] ).
cnf(166,axiom,
aNaturalNumber0(xn),
file('NUM487+1.p',unknown),
[] ).
cnf(168,axiom,
aNaturalNumber0(xp),
file('NUM487+1.p',unknown),
[] ).
cnf(169,axiom,
isPrime0(xp),
file('NUM487+1.p',unknown),
[] ).
cnf(171,axiom,
sdtlse_qdt0(xp,xn),
file('NUM487+1.p',unknown),
[] ).
cnf(172,axiom,
xr = sdtmndt0(xn,xp),
file('NUM487+1.p',unknown),
[] ).
cnf(174,plain,
sdtmndt0(xn,xp) = xr,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[172])]),
[iquote('copy,172,flip.1')] ).
cnf(189,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(hyper,[status(thm)],[164,13]),
[iquote('hyper,164,13')] ).
cnf(191,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(hyper,[status(thm)],[164,11]),
[iquote('hyper,164,11')] ).
cnf(193,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(hyper,[status(thm)],[164,8]),
[iquote('hyper,164,8')] ).
cnf(208,plain,
sdtasdt0(sdtpldt0(sz10,sz10),sz00) = sz00,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[165,87,164]),189,189,193])]),
[iquote('hyper,165,87,164,demod,189,189,193,flip.1')] ).
cnf(219,plain,
sdtasdt0(sz00,sdtpldt0(sz10,sz10)) = sz00,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[165,84,164]),191,191,193])]),
[iquote('hyper,165,84,164,demod,191,191,193,flip.1')] ).
cnf(245,plain,
aNaturalNumber0(sdtpldt0(sz10,sz10)),
inference(hyper,[status(thm)],[165,72]),
[iquote('hyper,165,72')] ).
cnf(248,plain,
sdtasdt0(sz10,sz10) = sz10,
inference(hyper,[status(thm)],[165,13]),
[iquote('hyper,165,13')] ).
cnf(250,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(hyper,[status(thm)],[165,8]),
[iquote('hyper,165,8')] ).
cnf(383,plain,
sdtlse_qdt0(xn,xn),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[166,38,166])]),
[iquote('hyper,166,38,166,factor_simp')] ).
cnf(424,plain,
sdtpldt0(xn,sz00) = xn,
inference(hyper,[status(thm)],[166,6]),
[iquote('hyper,166,6')] ).
cnf(987,plain,
sdtpldt0(sdtasdt0(xp,sz10),sdtasdt0(xp,sz10)) = sdtasdt0(sdtpldt0(xp,xp),sz10),
inference(hyper,[status(thm)],[168,87,165]),
[iquote('hyper,168,87,165')] ).
cnf(1043,plain,
sdtasdt0(sdtpldt0(xp,xp),sz10) = sdtasdt0(xp,sdtpldt0(sz10,sz10)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[168,84,165]),987]),
[iquote('hyper,168,84,165,demod,987')] ).
cnf(1342,plain,
sdtasdt0(xp,sz10) = xp,
inference(hyper,[status(thm)],[168,11]),
[iquote('hyper,168,11')] ).
cnf(1479,plain,
sdtpldt0(xp,xp) = sdtasdt0(xp,sdtpldt0(sz10,sz10)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[987]),1342,1342,1043]),
[iquote('back_demod,986,demod,1342,1342,1043')] ).
cnf(1753,plain,
( isPrime0(sz00)
| sdtasdt0(xp,sdtpldt0(sz10,sz10)) != sz00 ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[169,102]),1479]),168]),
[iquote('para_into,169.1.1,102.3.1,demod,1479,unit_del,168')] ).
cnf(1811,plain,
sdtpldt0(xp,xr) = xn,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[171,32,168,166,163]),174]),
[iquote('hyper,171,32,168,166,163,demod,174')] ).
cnf(1812,plain,
aNaturalNumber0(xr),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[171,31,168,166,163]),174]),
[iquote('hyper,171,31,168,166,163,demod,174')] ).
cnf(2704,plain,
sdtpldt0(xr,xp) = xn,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1812,4,168]),1811])]),
[iquote('hyper,1812,4,168,demod,1811,flip.1')] ).
cnf(4609,plain,
sdtpldt0(sz10,sz10) != sz00,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[248,102]),191]),1,165]),
[iquote('para_into,248.1.1.1,102.3.1,demod,191,unit_del,1,165')] ).
cnf(4644,plain,
doDivides0(sdtpldt0(sz10,sz10),sz00),
inference(hyper,[status(thm)],[208,129,245,164]),
[iquote('hyper,208,129,245,164')] ).
cnf(4646,plain,
sdtpldt0(sz10,sz10) != sz10,
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[250,92]),165,164,1])]),
[iquote('para_from,250.1.1,92.3.1,unit_del,165,164,1,flip.1')] ).
cnf(4800,plain,
sdtmndt0(xn,xn) = sz00,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[424,110,166,383,164])]),
[iquote('hyper,424,110,166,383,164,flip.1')] ).
cnf(5161,plain,
sdtlse_qdt0(xr,xn),
inference(hyper,[status(thm)],[2704,30,1812,166,168]),
[iquote('hyper,2704,30,1812,166,168')] ).
cnf(5162,plain,
sdtpldt0(xn,xp) = xn,
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[2704,71]),5161]),
[iquote('para_into,2704.1.1.1,71.1.1,unit_del,5161')] ).
cnf(5236,plain,
xp = sz00,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[5162,110,166,383,168]),4800]),
[iquote('hyper,5162,110,166,383,168,demod,4800')] ).
cnf(5242,plain,
isPrime0(sz00),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1753]),5236,219]),163]),
[iquote('back_demod,1753,demod,5236,219,unit_del,163')] ).
cnf(5244,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5242,62,164,245,4644]),4646,4609]),
[iquote('hyper,5242,62,164,245,4644,unit_del,4646,4609')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM487+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 09:47:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.13/2.31 ----- Otter 3.3f, August 2004 -----
% 2.13/2.31 The process was started by sandbox2 on n022.cluster.edu,
% 2.13/2.31 Wed Jul 27 09:47:05 2022
% 2.13/2.31 The command was "./otter". The process ID is 5961.
% 2.13/2.31
% 2.13/2.31 set(prolog_style_variables).
% 2.13/2.31 set(auto).
% 2.13/2.31 dependent: set(auto1).
% 2.13/2.31 dependent: set(process_input).
% 2.13/2.31 dependent: clear(print_kept).
% 2.13/2.31 dependent: clear(print_new_demod).
% 2.13/2.31 dependent: clear(print_back_demod).
% 2.13/2.31 dependent: clear(print_back_sub).
% 2.13/2.31 dependent: set(control_memory).
% 2.13/2.31 dependent: assign(max_mem, 12000).
% 2.13/2.31 dependent: assign(pick_given_ratio, 4).
% 2.13/2.31 dependent: assign(stats_level, 1).
% 2.13/2.31 dependent: assign(max_seconds, 10800).
% 2.13/2.31 clear(print_given).
% 2.13/2.31
% 2.13/2.31 formula_list(usable).
% 2.13/2.31 all A (A=A).
% 2.13/2.31 all W0 (aNaturalNumber0(W0)->$T).
% 2.13/2.31 aNaturalNumber0(sz00).
% 2.13/2.31 aNaturalNumber0(sz10).
% 2.13/2.31 sz10!=sz00.
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->aNaturalNumber0(sdtpldt0(W0,W1))).
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->aNaturalNumber0(sdtasdt0(W0,W1))).
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->sdtpldt0(W0,W1)=sdtpldt0(W1,W0)).
% 2.13/2.31 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)->sdtpldt0(sdtpldt0(W0,W1),W2)=sdtpldt0(W0,sdtpldt0(W1,W2))).
% 2.13/2.31 all W0 (aNaturalNumber0(W0)->sdtpldt0(W0,sz00)=W0&W0=sdtpldt0(sz00,W0)).
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->sdtasdt0(W0,W1)=sdtasdt0(W1,W0)).
% 2.13/2.31 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)->sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2))).
% 2.13/2.31 all W0 (aNaturalNumber0(W0)->sdtasdt0(W0,sz10)=W0&W0=sdtasdt0(sz10,W0)).
% 2.13/2.31 all W0 (aNaturalNumber0(W0)->sdtasdt0(W0,sz00)=sz00&sz00=sdtasdt0(sz00,W0)).
% 2.13/2.31 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)->sdtasdt0(W0,sdtpldt0(W1,W2))=sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))&sdtasdt0(sdtpldt0(W1,W2),W0)=sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))).
% 2.13/2.31 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (sdtpldt0(W0,W1)=sdtpldt0(W0,W2)|sdtpldt0(W1,W0)=sdtpldt0(W2,W0)->W1=W2)).
% 2.13/2.31 all W0 (aNaturalNumber0(W0)-> (W0!=sz00-> (all W1 W2 (aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (sdtasdt0(W0,W1)=sdtasdt0(W0,W2)|sdtasdt0(W1,W0)=sdtasdt0(W2,W0)->W1=W2))))).
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtpldt0(W0,W1)=sz00->W0=sz00&W1=sz00)).
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtasdt0(W0,W1)=sz00->W0=sz00|W1=sz00)).
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtlse_qdt0(W0,W1)<-> (exists W2 (aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1)))).
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtlse_qdt0(W0,W1)-> (all W2 (W2=sdtmndt0(W1,W0)<->aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1)))).
% 2.13/2.31 all W0 (aNaturalNumber0(W0)->sdtlse_qdt0(W0,W0)).
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtlse_qdt0(W0,W1)&sdtlse_qdt0(W1,W0)->W0=W1)).
% 2.13/2.31 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (sdtlse_qdt0(W0,W1)&sdtlse_qdt0(W1,W2)->sdtlse_qdt0(W0,W2))).
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->sdtlse_qdt0(W0,W1)|W1!=W0&sdtlse_qdt0(W1,W0)).
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (W0!=W1&sdtlse_qdt0(W0,W1)-> (all W2 (aNaturalNumber0(W2)->sdtpldt0(W2,W0)!=sdtpldt0(W2,W1)&sdtlse_qdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))&sdtpldt0(W0,W2)!=sdtpldt0(W1,W2)&sdtlse_qdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)))))).
% 2.13/2.31 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (W0!=sz00&W1!=W2&sdtlse_qdt0(W1,W2)->sdtasdt0(W0,W1)!=sdtasdt0(W0,W2)&sdtlse_qdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))&sdtasdt0(W1,W0)!=sdtasdt0(W2,W0)&sdtlse_qdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)))).
% 2.13/2.31 all W0 (aNaturalNumber0(W0)->W0=sz00|W0=sz10|sz10!=W0&sdtlse_qdt0(sz10,W0)).
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (W0!=sz00->sdtlse_qdt0(W1,sdtasdt0(W1,W0)))).
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (iLess0(W0,W1)->$T)).
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (W0!=W1&sdtlse_qdt0(W0,W1)->iLess0(W0,W1))).
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (doDivides0(W0,W1)<-> (exists W2 (aNaturalNumber0(W2)&W1=sdtasdt0(W0,W2))))).
% 2.13/2.31 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (W0!=sz00&doDivides0(W0,W1)-> (all W2 (W2=sdtsldt0(W1,W0)<->aNaturalNumber0(W2)&W1=sdtasdt0(W0,W2))))).
% 2.13/2.32 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (doDivides0(W0,W1)&doDivides0(W1,W2)->doDivides0(W0,W2))).
% 2.13/2.32 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (doDivides0(W0,W1)&doDivides0(W0,W2)->doDivides0(W0,sdtpldt0(W1,W2)))).
% 2.13/2.32 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (doDivides0(W0,W1)&doDivides0(W0,sdtpldt0(W1,W2))->doDivides0(W0,W2))).
% 2.13/2.32 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (doDivides0(W0,W1)&W1!=sz00->sdtlse_qdt0(W0,W1))).
% 2.13/2.32 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (W0!=sz00&doDivides0(W0,W1)-> (all W2 (aNaturalNumber0(W2)->sdtasdt0(W2,sdtsldt0(W1,W0))=sdtsldt0(sdtasdt0(W2,W1),W0))))).
% 2.13/2.32 all W0 (aNaturalNumber0(W0)-> (isPrime0(W0)<->W0!=sz00&W0!=sz10& (all W1 (aNaturalNumber0(W1)&doDivides0(W1,W0)->W1=sz10|W1=W0)))).
% 2.13/2.32 all W0 (aNaturalNumber0(W0)&W0!=sz00&W0!=sz10-> (exists W1 (aNaturalNumber0(W1)&doDivides0(W1,W0)&isPrime0(W1)))).
% 2.13/2.32 aNaturalNumber0(xn).
% 2.13/2.32 aNaturalNumber0(xm).
% 2.13/2.32 aNaturalNumber0(xp).
% 2.13/2.32 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (isPrime0(W2)&doDivides0(W2,sdtasdt0(W0,W1))-> (iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))->doDivides0(W2,W0)|doDivides0(W2,W1)))).
% 2.13/2.32 isPrime0(xp).
% 2.13/2.32 doDivides0(xp,sdtasdt0(xn,xm)).
% 2.13/2.32 sdtlse_qdt0(xp,xn).
% 2.13/2.32 xr=sdtmndt0(xn,xp).
% 2.13/2.32 -(xr!=xn&sdtlse_qdt0(xr,xn)).
% 2.13/2.32 end_of_list.
% 2.13/2.32
% 2.13/2.32 -------> usable clausifies to:
% 2.13/2.32
% 2.13/2.32 list(usable).
% 2.13/2.32 0 [] A=A.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|$T.
% 2.13/2.32 0 [] aNaturalNumber0(sz00).
% 2.13/2.32 0 [] aNaturalNumber0(sz10).
% 2.13/2.32 0 [] sz10!=sz00.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|aNaturalNumber0(sdtpldt0(W0,W1)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|aNaturalNumber0(sdtasdt0(W0,W1)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtpldt0(W0,W1)=sdtpldt0(W1,W0).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtpldt0(sdtpldt0(W0,W1),W2)=sdtpldt0(W0,sdtpldt0(W1,W2)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|sdtpldt0(W0,sz00)=W0.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|W0=sdtpldt0(sz00,W0).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtasdt0(W0,W1)=sdtasdt0(W1,W0).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|sdtasdt0(W0,sz10)=W0.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|W0=sdtasdt0(sz10,W0).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|sdtasdt0(W0,sz00)=sz00.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|sz00=sdtasdt0(sz00,W0).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(W0,sdtpldt0(W1,W2))=sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(sdtpldt0(W1,W2),W0)=sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtpldt0(W0,W1)!=sdtpldt0(W0,W2)|W1=W2.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtpldt0(W1,W0)!=sdtpldt0(W2,W0)|W1=W2.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|W0=sz00| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(W0,W1)!=sdtasdt0(W0,W2)|W1=W2.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|W0=sz00| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(W1,W0)!=sdtasdt0(W2,W0)|W1=W2.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtpldt0(W0,W1)!=sz00|W0=sz00.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtpldt0(W0,W1)!=sz00|W1=sz00.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtasdt0(W0,W1)!=sz00|W0=sz00|W1=sz00.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|aNaturalNumber0($f1(W0,W1)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|sdtpldt0(W0,$f1(W0,W1))=W1.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtpldt0(W0,W2)!=W1.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|W2!=sdtmndt0(W1,W0)|aNaturalNumber0(W2).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|W2!=sdtmndt0(W1,W0)|sdtpldt0(W0,W2)=W1.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|W2=sdtmndt0(W1,W0)| -aNaturalNumber0(W2)|sdtpldt0(W0,W2)!=W1.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|sdtlse_qdt0(W0,W0).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)| -sdtlse_qdt0(W1,W0)|W0=W1.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)| -sdtlse_qdt0(W0,W1)| -sdtlse_qdt0(W1,W2)|sdtlse_qdt0(W0,W2).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtlse_qdt0(W0,W1)|W1!=W0.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtlse_qdt0(W0,W1)|sdtlse_qdt0(W1,W0).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtpldt0(W2,W0)!=sdtpldt0(W2,W1).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtlse_qdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtpldt0(W0,W2)!=sdtpldt0(W1,W2).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtlse_qdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtasdt0(W0,W1)!=sdtasdt0(W0,W2).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtlse_qdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtasdt0(W1,W0)!=sdtasdt0(W2,W0).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtlse_qdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|W0=sz00|W0=sz10|sz10!=W0.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|W0=sz00|W0=sz10|sdtlse_qdt0(sz10,W0).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=sz00|sdtlse_qdt0(W1,sdtasdt0(W1,W0)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -iLess0(W0,W1)|$T.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)|iLess0(W0,W1).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -doDivides0(W0,W1)|aNaturalNumber0($f2(W0,W1)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -doDivides0(W0,W1)|W1=sdtasdt0(W0,$f2(W0,W1)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|doDivides0(W0,W1)| -aNaturalNumber0(W2)|W1!=sdtasdt0(W0,W2).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=sz00| -doDivides0(W0,W1)|W2!=sdtsldt0(W1,W0)|aNaturalNumber0(W2).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=sz00| -doDivides0(W0,W1)|W2!=sdtsldt0(W1,W0)|W1=sdtasdt0(W0,W2).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=sz00| -doDivides0(W0,W1)|W2=sdtsldt0(W1,W0)| -aNaturalNumber0(W2)|W1!=sdtasdt0(W0,W2).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)| -doDivides0(W0,W1)| -doDivides0(W1,W2)|doDivides0(W0,W2).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)| -doDivides0(W0,W1)| -doDivides0(W0,W2)|doDivides0(W0,sdtpldt0(W1,W2)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)| -doDivides0(W0,W1)| -doDivides0(W0,sdtpldt0(W1,W2))|doDivides0(W0,W2).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -doDivides0(W0,W1)|W1=sz00|sdtlse_qdt0(W0,W1).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=sz00| -doDivides0(W0,W1)| -aNaturalNumber0(W2)|sdtasdt0(W2,sdtsldt0(W1,W0))=sdtsldt0(sdtasdt0(W2,W1),W0).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -isPrime0(W0)|W0!=sz00.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -isPrime0(W0)|W0!=sz10.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -isPrime0(W0)| -aNaturalNumber0(W1)| -doDivides0(W1,W0)|W1=sz10|W1=W0.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|isPrime0(W0)|W0=sz00|W0=sz10|aNaturalNumber0($f3(W0)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|isPrime0(W0)|W0=sz00|W0=sz10|doDivides0($f3(W0),W0).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|isPrime0(W0)|W0=sz00|W0=sz10|$f3(W0)!=sz10.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|isPrime0(W0)|W0=sz00|W0=sz10|$f3(W0)!=W0.
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|W0=sz00|W0=sz10|aNaturalNumber0($f4(W0)).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|W0=sz00|W0=sz10|doDivides0($f4(W0),W0).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)|W0=sz00|W0=sz10|isPrime0($f4(W0)).
% 2.13/2.32 0 [] aNaturalNumber0(xn).
% 2.13/2.32 0 [] aNaturalNumber0(xm).
% 2.13/2.32 0 [] aNaturalNumber0(xp).
% 2.13/2.32 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)| -isPrime0(W2)| -doDivides0(W2,sdtasdt0(W0,W1))| -iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))|doDivides0(W2,W0)|doDivides0(W2,W1).
% 2.13/2.32 0 [] isPrime0(xp).
% 2.13/2.32 0 [] doDivides0(xp,sdtasdt0(xn,xm)).
% 2.13/2.32 0 [] sdtlse_qdt0(xp,xn).
% 2.13/2.32 0 [] xr=sdtmndt0(xn,xp).
% 2.13/2.32 0 [] xr=xn| -sdtlse_qdt0(xr,xn).
% 2.13/2.32 end_of_list.
% 2.13/2.32
% 2.13/2.32 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 2.13/2.32
% 2.13/2.32 This ia a non-Horn set with equality. The strategy will be
% 2.13/2.32 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.13/2.32 deletion, with positive clauses in sos and nonpositive
% 2.13/2.32 clauses in usable.
% 2.13/2.32
% 2.13/2.32 dependent: set(knuth_bendix).
% 2.13/2.32 dependent: set(anl_eq).
% 2.13/2.32 dependent: set(para_from).
% 2.13/2.32 dependent: set(para_into).
% 2.13/2.32 dependent: clear(para_from_right).
% 2.13/2.32 dependent: clear(para_into_right).
% 2.13/2.32 dependent: set(para_from_vars).
% 2.13/2.32 dependent: set(eq_units_both_ways).
% 2.13/2.32 dependent: set(dynamic_demod_all).
% 2.13/2.32 dependent: set(dynamic_demod).
% 2.13/2.32 dependent: set(order_eq).
% 2.13/2.32 dependent: set(back_demod).
% 2.13/2.32 dependent: set(lrpo).
% 2.13/2.32 dependent: set(hyper_res).
% 2.13/2.32 dependent: set(unit_deletion).
% 2.13/2.32 dependent: set(factor).
% 2.13/2.32
% 2.13/2.32 ------------> process usable:
% 2.13/2.32 ** KEPT (pick-wt=3): 1 [] sz10!=sz00.
% 2.13/2.32 ** KEPT (pick-wt=8): 2 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|aNaturalNumber0(sdtpldt0(A,B)).
% 2.13/2.32 ** KEPT (pick-wt=8): 3 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|aNaturalNumber0(sdtasdt0(A,B)).
% 2.13/2.32 ** KEPT (pick-wt=11): 4 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtpldt0(A,B)=sdtpldt0(B,A).
% 2.13/2.32 ** KEPT (pick-wt=17): 5 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(sdtpldt0(A,B),C)=sdtpldt0(A,sdtpldt0(B,C)).
% 2.13/2.32 ** KEPT (pick-wt=7): 6 [] -aNaturalNumber0(A)|sdtpldt0(A,sz00)=A.
% 2.13/2.32 ** KEPT (pick-wt=7): 8 [copy,7,flip.2] -aNaturalNumber0(A)|sdtpldt0(sz00,A)=A.
% 2.13/2.32 ** KEPT (pick-wt=11): 9 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtasdt0(A,B)=sdtasdt0(B,A).
% 2.13/2.32 ** KEPT (pick-wt=17): 10 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtasdt0(sdtasdt0(A,B),C)=sdtasdt0(A,sdtasdt0(B,C)).
% 2.13/2.32 ** KEPT (pick-wt=7): 11 [] -aNaturalNumber0(A)|sdtasdt0(A,sz10)=A.
% 2.13/2.32 ** KEPT (pick-wt=7): 13 [copy,12,flip.2] -aNaturalNumber0(A)|sdtasdt0(sz10,A)=A.
% 2.13/2.32 ** KEPT (pick-wt=7): 14 [] -aNaturalNumber0(A)|sdtasdt0(A,sz00)=sz00.
% 2.13/2.32 ** KEPT (pick-wt=7): 16 [copy,15,flip.2] -aNaturalNumber0(A)|sdtasdt0(sz00,A)=sz00.
% 2.13/2.32 ** KEPT (pick-wt=19): 18 [copy,17,flip.4] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C))=sdtasdt0(A,sdtpldt0(B,C)).
% 2.13/2.32 ** KEPT (pick-wt=19): 20 [copy,19,flip.4] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(sdtasdt0(B,A),sdtasdt0(C,A))=sdtasdt0(sdtpldt0(B,C),A).
% 2.13/2.32 ** KEPT (pick-wt=16): 21 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(A,B)!=sdtpldt0(A,C)|B=C.
% 2.13/2.32 ** KEPT (pick-wt=16): 22 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(B,A)!=sdtpldt0(C,A)|B=C.
% 2.13/2.32 ** KEPT (pick-wt=19): 23 [] -aNaturalNumber0(A)|A=sz00| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtasdt0(A,B)!=sdtasdt0(A,C)|B=C.
% 2.13/2.32 ** KEPT (pick-wt=19): 24 [] -aNaturalNumber0(A)|A=sz00| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtasdt0(B,A)!=sdtasdt0(C,A)|B=C.
% 2.13/2.32 ** KEPT (pick-wt=12): 25 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtpldt0(A,B)!=sz00|A=sz00.
% 2.13/2.32 ** KEPT (pick-wt=12): 26 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtpldt0(A,B)!=sz00|B=sz00.
% 2.13/2.32 ** KEPT (pick-wt=15): 27 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtasdt0(A,B)!=sz00|A=sz00|B=sz00.
% 2.13/2.32 ** KEPT (pick-wt=11): 28 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|aNaturalNumber0($f1(A,B)).
% 2.13/2.32 ** KEPT (pick-wt=14): 29 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|sdtpldt0(A,$f1(A,B))=B.
% 2.13/2.32 ** KEPT (pick-wt=14): 30 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtpldt0(A,C)!=B.
% 2.13/2.32 ** KEPT (pick-wt=14): 31 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|C!=sdtmndt0(B,A)|aNaturalNumber0(C).
% 2.13/2.32 ** KEPT (pick-wt=17): 32 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|C!=sdtmndt0(B,A)|sdtpldt0(A,C)=B.
% 2.13/2.32 ** KEPT (pick-wt=19): 33 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|C=sdtmndt0(B,A)| -aNaturalNumber0(C)|sdtpldt0(A,C)!=B.
% 2.13/2.35 ** KEPT (pick-wt=5): 34 [] -aNaturalNumber0(A)|sdtlse_qdt0(A,A).
% 2.13/2.35 ** KEPT (pick-wt=13): 35 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)| -sdtlse_qdt0(B,A)|A=B.
% 2.13/2.35 ** KEPT (pick-wt=15): 36 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)| -sdtlse_qdt0(A,B)| -sdtlse_qdt0(B,C)|sdtlse_qdt0(A,C).
% 2.13/2.35 ** KEPT (pick-wt=10): 37 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtlse_qdt0(A,B)|B!=A.
% 2.13/2.35 ** KEPT (pick-wt=10): 38 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtlse_qdt0(A,B)|sdtlse_qdt0(B,A).
% 2.13/2.35 Following clause subsumed by 21 during input processing: 0 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=B| -sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtpldt0(C,A)!=sdtpldt0(C,B).
% 2.13/2.35 ** KEPT (pick-wt=19): 39 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=B| -sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtlse_qdt0(sdtpldt0(C,A),sdtpldt0(C,B)).
% 2.13/2.35 Following clause subsumed by 22 during input processing: 0 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=B| -sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtpldt0(A,C)!=sdtpldt0(B,C).
% 2.13/2.35 ** KEPT (pick-wt=19): 40 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=B| -sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtlse_qdt0(sdtpldt0(A,C),sdtpldt0(B,C)).
% 2.13/2.35 Following clause subsumed by 23 during input processing: 0 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|A=sz00|B=C| -sdtlse_qdt0(B,C)|sdtasdt0(A,B)!=sdtasdt0(A,C).
% 2.13/2.35 ** KEPT (pick-wt=22): 41 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|A=sz00|B=C| -sdtlse_qdt0(B,C)|sdtlse_qdt0(sdtasdt0(A,B),sdtasdt0(A,C)).
% 2.13/2.35 Following clause subsumed by 24 during input processing: 0 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|A=sz00|B=C| -sdtlse_qdt0(B,C)|sdtasdt0(B,A)!=sdtasdt0(C,A).
% 2.13/2.35 ** KEPT (pick-wt=22): 42 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|A=sz00|B=C| -sdtlse_qdt0(B,C)|sdtlse_qdt0(sdtasdt0(B,A),sdtasdt0(C,A)).
% 2.13/2.35 ** KEPT (pick-wt=11): 43 [] -aNaturalNumber0(A)|A=sz00|A=sz10|sz10!=A.
% 2.13/2.35 ** KEPT (pick-wt=11): 44 [] -aNaturalNumber0(A)|A=sz00|A=sz10|sdtlse_qdt0(sz10,A).
% 2.13/2.35 ** KEPT (pick-wt=12): 45 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=sz00|sdtlse_qdt0(B,sdtasdt0(B,A)).
% 2.13/2.35 ** KEPT (pick-wt=13): 46 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=B| -sdtlse_qdt0(A,B)|iLess0(A,B).
% 2.13/2.35 ** KEPT (pick-wt=11): 47 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -doDivides0(A,B)|aNaturalNumber0($f2(A,B)).
% 2.13/2.35 ** KEPT (pick-wt=14): 49 [copy,48,flip.4] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -doDivides0(A,B)|sdtasdt0(A,$f2(A,B))=B.
% 2.13/2.35 ** KEPT (pick-wt=14): 50 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|doDivides0(A,B)| -aNaturalNumber0(C)|B!=sdtasdt0(A,C).
% 2.13/2.35 ** KEPT (pick-wt=17): 51 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=sz00| -doDivides0(A,B)|C!=sdtsldt0(B,A)|aNaturalNumber0(C).
% 2.13/2.35 ** KEPT (pick-wt=20): 52 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=sz00| -doDivides0(A,B)|C!=sdtsldt0(B,A)|B=sdtasdt0(A,C).
% 2.13/2.35 ** KEPT (pick-wt=22): 53 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=sz00| -doDivides0(A,B)|C=sdtsldt0(B,A)| -aNaturalNumber0(C)|B!=sdtasdt0(A,C).
% 2.13/2.35 ** KEPT (pick-wt=15): 54 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)| -doDivides0(A,B)| -doDivides0(B,C)|doDivides0(A,C).
% 2.13/2.35 ** KEPT (pick-wt=17): 55 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)| -doDivides0(A,B)| -doDivides0(A,C)|doDivides0(A,sdtpldt0(B,C)).
% 2.13/2.35 ** KEPT (pick-wt=17): 56 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)| -doDivides0(A,B)| -doDivides0(A,sdtpldt0(B,C))|doDivides0(A,C).
% 2.13/2.35 ** KEPT (pick-wt=13): 57 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -doDivides0(A,B)|B=sz00|sdtlse_qdt0(A,B).
% 2.13/2.35 ** KEPT (pick-wt=23): 59 [copy,58,flip.6] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=sz00| -doDivides0(A,B)| -aNaturalNumber0(C)|sdtsldt0(sdtasdt0(C,B),A)=sdtasdt0(C,sdtsldt0(B,A)).
% 2.13/2.35 ** KEPT (pick-wt=7): 60 [] -aNaturalNumber0(A)| -isPrime0(A)|A!=sz00.
% 2.13/2.35 ** KEPT (pick-wt=7): 61 [] -aNaturalNumber0(A)| -isPrime0(A)|A!=sz10.
% 2.13/2.35 ** KEPT (pick-wt=15): 62 [] -aNaturalNumber0(A)| -isPrime0(A)| -aNaturalNumber0(B)| -doDivides0(B,A)|B=sz10|B=A.
% 15.34/15.56 ** KEPT (pick-wt=13): 63 [] -aNaturalNumber0(A)|isPrime0(A)|A=sz00|A=sz10|aNaturalNumber0($f3(A)).
% 15.34/15.56 ** KEPT (pick-wt=14): 64 [] -aNaturalNumber0(A)|isPrime0(A)|A=sz00|A=sz10|doDivides0($f3(A),A).
% 15.34/15.56 ** KEPT (pick-wt=14): 65 [] -aNaturalNumber0(A)|isPrime0(A)|A=sz00|A=sz10|$f3(A)!=sz10.
% 15.34/15.56 ** KEPT (pick-wt=14): 66 [] -aNaturalNumber0(A)|isPrime0(A)|A=sz00|A=sz10|$f3(A)!=A.
% 15.34/15.56 ** KEPT (pick-wt=11): 67 [] -aNaturalNumber0(A)|A=sz00|A=sz10|aNaturalNumber0($f4(A)).
% 15.34/15.56 ** KEPT (pick-wt=12): 68 [] -aNaturalNumber0(A)|A=sz00|A=sz10|doDivides0($f4(A),A).
% 15.34/15.56 ** KEPT (pick-wt=11): 69 [] -aNaturalNumber0(A)|A=sz00|A=sz10|isPrime0($f4(A)).
% 15.34/15.56 ** KEPT (pick-wt=30): 70 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)| -isPrime0(C)| -doDivides0(C,sdtasdt0(A,B))| -iLess0(sdtpldt0(sdtpldt0(A,B),C),sdtpldt0(sdtpldt0(xn,xm),xp))|doDivides0(C,A)|doDivides0(C,B).
% 15.34/15.56 ** KEPT (pick-wt=6): 71 [] xr=xn| -sdtlse_qdt0(xr,xn).
% 15.34/15.56
% 15.34/15.56 ------------> process sos:
% 15.34/15.56 ** KEPT (pick-wt=3): 163 [] A=A.
% 15.34/15.56 ** KEPT (pick-wt=2): 164 [] aNaturalNumber0(sz00).
% 15.34/15.56 ** KEPT (pick-wt=2): 165 [] aNaturalNumber0(sz10).
% 15.34/15.56 ** KEPT (pick-wt=2): 166 [] aNaturalNumber0(xn).
% 15.34/15.56 ** KEPT (pick-wt=2): 167 [] aNaturalNumber0(xm).
% 15.34/15.56 ** KEPT (pick-wt=2): 168 [] aNaturalNumber0(xp).
% 15.34/15.56 ** KEPT (pick-wt=2): 169 [] isPrime0(xp).
% 15.34/15.56 ** KEPT (pick-wt=5): 170 [] doDivides0(xp,sdtasdt0(xn,xm)).
% 15.34/15.56 ** KEPT (pick-wt=3): 171 [] sdtlse_qdt0(xp,xn).
% 15.34/15.56 ** KEPT (pick-wt=5): 173 [copy,172,flip.1] sdtmndt0(xn,xp)=xr.
% 15.34/15.56 ---> New Demodulator: 174 [new_demod,173] sdtmndt0(xn,xp)=xr.
% 15.34/15.56 Following clause subsumed by 163 during input processing: 0 [copy,163,flip.1] A=A.
% 15.34/15.56 163 back subsumes 161.
% 15.34/15.56 163 back subsumes 155.
% 15.34/15.56 163 back subsumes 154.
% 15.34/15.56 163 back subsumes 153.
% 15.34/15.56 163 back subsumes 144.
% 15.34/15.56 163 back subsumes 113.
% 15.34/15.56 163 back subsumes 101.
% 15.34/15.56 163 back subsumes 97.
% 15.34/15.56 163 back subsumes 93.
% 15.34/15.56 163 back subsumes 90.
% 15.34/15.56 163 back subsumes 78.
% 15.34/15.56 163 back subsumes 74.
% 15.34/15.56 >>>> Starting back demodulation with 174.
% 15.34/15.56
% 15.34/15.56 ======= end of input processing =======
% 15.34/15.56
% 15.34/15.56 =========== start of search ===========
% 15.34/15.56
% 15.34/15.56
% 15.34/15.56 Resetting weight limit to 7.
% 15.34/15.56
% 15.34/15.56
% 15.34/15.56 Resetting weight limit to 7.
% 15.34/15.56
% 15.34/15.56 sos_size=1932
% 15.34/15.56
% 15.34/15.56
% 15.34/15.56 Resetting weight limit to 6.
% 15.34/15.56
% 15.34/15.56
% 15.34/15.56 Resetting weight limit to 6.
% 15.34/15.56
% 15.34/15.56 sos_size=2064
% 15.34/15.56
% 15.34/15.56 -- HEY sandbox2, WE HAVE A PROOF!! --
% 15.34/15.56
% 15.34/15.56 -----> EMPTY CLAUSE at 13.24 sec ----> 5244 [hyper,5242,62,164,245,4644,unit_del,4646,4609] $F.
% 15.34/15.56
% 15.34/15.56 Length of proof is 38. Level of proof is 7.
% 15.34/15.56
% 15.34/15.56 ---------------- PROOF ----------------
% 15.34/15.56 % SZS status Theorem
% 15.34/15.56 % SZS output start Refutation
% See solution above
% 15.34/15.56 ------------ end of proof -------------
% 15.34/15.56
% 15.34/15.56
% 15.34/15.56 Search stopped by max_proofs option.
% 15.34/15.56
% 15.34/15.56
% 15.34/15.56 Search stopped by max_proofs option.
% 15.34/15.56
% 15.34/15.56 ============ end of search ============
% 15.34/15.56
% 15.34/15.56 -------------- statistics -------------
% 15.34/15.56 clauses given 207
% 15.34/15.56 clauses generated 895993
% 15.34/15.56 clauses kept 3953
% 15.34/15.56 clauses forward subsumed 13638
% 15.34/15.56 clauses back subsumed 291
% 15.34/15.56 Kbytes malloced 5859
% 15.34/15.56
% 15.34/15.56 ----------- times (seconds) -----------
% 15.34/15.56 user CPU time 13.25 (0 hr, 0 min, 13 sec)
% 15.34/15.56 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 15.34/15.56 wall-clock time 15 (0 hr, 0 min, 15 sec)
% 15.34/15.56
% 15.34/15.56 That finishes the proof of the theorem.
% 15.34/15.56
% 15.34/15.56 Process 5961 finished Wed Jul 27 09:47:20 2022
% 15.34/15.56 Otter interrupted
% 15.34/15.56 PROOF FOUND
%------------------------------------------------------------------------------