TSTP Solution File: NUM457+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM457+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 13:08:25 EDT 2022
% Result : Theorem 15.32s 15.53s
% Output : Refutation 15.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of clauses : 58 ( 36 unt; 4 nHn; 58 RR)
% Number of literals : 110 ( 59 equ; 51 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| aNaturalNumber0(sdtpldt0(A,B)) ),
file('NUM457+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| sdtpldt0(A,B) = sdtpldt0(B,A) ),
file('NUM457+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ aNaturalNumber0(A)
| sdtpldt0(A,sz00) = A ),
file('NUM457+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ aNaturalNumber0(A)
| A = sdtpldt0(sz00,A) ),
file('NUM457+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(9,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| sdtasdt0(A,B) = sdtasdt0(B,A) ),
file('NUM457+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ aNaturalNumber0(A)
| sdtasdt0(A,sz10) = A ),
file('NUM457+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ aNaturalNumber0(A)
| sz00 = sdtasdt0(sz00,A) ),
file('NUM457+1.p',unknown),
[] ).
cnf(16,plain,
( ~ aNaturalNumber0(A)
| sdtasdt0(sz00,A) = sz00 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.2')] ).
cnf(17,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(C)
| sdtasdt0(A,sdtpldt0(B,C)) = sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) ),
file('NUM457+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('NUM457+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(23,axiom,
( ~ aNaturalNumber0(A)
| A = sz00
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(C)
| sdtasdt0(A,B) != sdtasdt0(A,C)
| B = C ),
file('NUM457+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ aNaturalNumber0(A)
| A = sz00
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(C)
| sdtasdt0(B,A) != sdtasdt0(C,A)
| B = C ),
file('NUM457+1.p',unknown),
[] ).
cnf(27,axiom,
xm != sz00,
file('NUM457+1.p',unknown),
[] ).
cnf(28,axiom,
xn != sz00,
file('NUM457+1.p',unknown),
[] ).
cnf(39,plain,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| sdtpldt0(sdtasdt0(A,A),sdtasdt0(A,B)) = sdtasdt0(A,sdtpldt0(A,B)) ),
inference(factor,[status(thm)],[18]),
[iquote('factor,18.1.2')] ).
cnf(41,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(42,plain,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| sdtpldt0(sdtasdt0(A,A),sdtasdt0(B,A)) = sdtasdt0(sdtpldt0(A,B),A) ),
inference(factor,[status(thm)],[20]),
[iquote('factor,20.1.2')] ).
cnf(43,plain,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| sdtpldt0(sdtasdt0(B,A),sdtasdt0(A,A)) = sdtasdt0(sdtpldt0(B,A),A) ),
inference(factor,[status(thm)],[20]),
[iquote('factor,20.1.3')] ).
cnf(44,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(52,plain,
( ~ aNaturalNumber0(A)
| A = sz00
| ~ aNaturalNumber0(B)
| sdtasdt0(A,B) != sdtasdt0(A,A)
| B = A ),
inference(factor,[status(thm)],[23]),
[iquote('factor,23.1.4')] ).
cnf(56,plain,
( ~ aNaturalNumber0(A)
| A = sz00
| ~ aNaturalNumber0(B)
| sdtasdt0(B,A) != sdtasdt0(A,A)
| B = A ),
inference(factor,[status(thm)],[24]),
[iquote('factor,24.1.4')] ).
cnf(68,axiom,
aNaturalNumber0(sz00),
file('NUM457+1.p',unknown),
[] ).
cnf(69,axiom,
aNaturalNumber0(sz10),
file('NUM457+1.p',unknown),
[] ).
cnf(70,axiom,
aNaturalNumber0(xm),
file('NUM457+1.p',unknown),
[] ).
cnf(71,axiom,
aNaturalNumber0(xn),
file('NUM457+1.p',unknown),
[] ).
cnf(73,axiom,
sdtasdt0(xm,xn) = sz00,
file('NUM457+1.p',unknown),
[] ).
cnf(91,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(hyper,[status(thm)],[68,8]),
[iquote('hyper,68,8')] ).
cnf(161,plain,
sdtpldt0(sdtasdt0(xm,sz10),sdtasdt0(xm,sz10)) = sdtasdt0(sdtpldt0(xm,xm),sz10),
inference(hyper,[status(thm)],[70,44,69]),
[iquote('hyper,70,44,69')] ).
cnf(182,plain,
sdtpldt0(sdtasdt0(xm,xm),sdtasdt0(sz00,xm)) = sdtasdt0(sdtpldt0(xm,sz00),xm),
inference(hyper,[status(thm)],[70,42,68]),
[iquote('hyper,70,42,68')] ).
cnf(189,plain,
sdtasdt0(sdtpldt0(xm,xm),sz10) = sdtasdt0(xm,sdtpldt0(sz10,sz10)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[70,41,69]),161]),
[iquote('hyper,70,41,69,demod,161')] ).
cnf(283,plain,
sdtasdt0(sz00,xm) = sz00,
inference(hyper,[status(thm)],[70,16]),
[iquote('hyper,70,16')] ).
cnf(289,plain,
sdtasdt0(xm,sz10) = xm,
inference(hyper,[status(thm)],[70,11]),
[iquote('hyper,70,11')] ).
cnf(297,plain,
sdtpldt0(xm,sz00) = xm,
inference(hyper,[status(thm)],[70,6]),
[iquote('hyper,70,6')] ).
cnf(314,plain,
sdtpldt0(xm,xm) = sdtasdt0(xm,sdtpldt0(sz10,sz10)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[161]),289,289,189]),
[iquote('back_demod,160,demod,289,289,189')] ).
cnf(320,plain,
sdtpldt0(sdtasdt0(xm,xm),sz00) = sdtasdt0(xm,xm),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[182]),283,297]),
[iquote('back_demod,182,demod,283,297')] ).
cnf(383,plain,
sdtpldt0(sdtasdt0(xn,xm),sdtasdt0(xn,xm)) = sdtasdt0(sdtpldt0(xn,xn),xm),
inference(hyper,[status(thm)],[71,44,70]),
[iquote('hyper,71,44,70')] ).
cnf(401,plain,
sdtasdt0(sdtpldt0(xm,xn),xn) = sdtpldt0(sz00,sdtasdt0(xn,xn)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[71,43,70]),73])]),
[iquote('hyper,71,43,70,demod,73,flip.1')] ).
cnf(413,plain,
sdtpldt0(sdtasdt0(xn,xn),sz00) = sdtasdt0(sdtpldt0(xn,xm),xn),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[71,42,70]),73]),
[iquote('hyper,71,42,70,demod,73')] ).
cnf(416,plain,
sdtpldt0(sdtasdt0(xn,xn),sdtasdt0(sz00,xn)) = sdtasdt0(sdtpldt0(xn,sz00),xn),
inference(hyper,[status(thm)],[71,42,68]),
[iquote('hyper,71,42,68')] ).
cnf(425,plain,
sdtasdt0(sdtpldt0(xn,xn),xm) = sdtasdt0(xn,sdtasdt0(xm,sdtpldt0(sz10,sz10))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[71,41,70]),383,314]),
[iquote('hyper,71,41,70,demod,383,314')] ).
cnf(442,plain,
sdtasdt0(xm,sdtpldt0(xm,xn)) = sdtasdt0(xm,xm),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[71,39,70]),73,320])]),
[iquote('hyper,71,39,70,demod,73,320,flip.1')] ).
cnf(448,plain,
sdtpldt0(sdtasdt0(xn,xn),sdtasdt0(xn,xm)) = sdtasdt0(xn,sdtpldt0(xn,xm)),
inference(hyper,[status(thm)],[71,39,70]),
[iquote('hyper,71,39,70')] ).
cnf(601,plain,
sdtasdt0(sz00,xn) = sz00,
inference(hyper,[status(thm)],[71,16]),
[iquote('hyper,71,16')] ).
cnf(621,plain,
sdtasdt0(xn,xm) = sz00,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[71,9,70]),73])]),
[iquote('hyper,71,9,70,demod,73,flip.1')] ).
cnf(625,plain,
sdtpldt0(xn,sz00) = xn,
inference(hyper,[status(thm)],[71,6]),
[iquote('hyper,71,6')] ).
cnf(657,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[71,4,70])]),
[iquote('hyper,71,4,70,flip.1')] ).
cnf(660,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(hyper,[status(thm)],[71,2,70]),
[iquote('hyper,71,2,70')] ).
cnf(665,plain,
sdtasdt0(xn,sdtasdt0(xm,sdtpldt0(sz10,sz10))) = sz00,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[383]),621,621,91,425])]),
[iquote('back_demod,382,demod,621,621,91,425,flip.1')] ).
cnf(677,plain,
sdtpldt0(sz00,sdtasdt0(xn,xn)) = sdtasdt0(xn,xn),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[416]),601,413,657,401,625]),
[iquote('back_demod,416,demod,601,413,657,401,625')] ).
cnf(707,plain,
sdtasdt0(xn,sdtpldt0(xm,xn)) = sdtasdt0(xn,xn),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[448]),621,413,657,401,677,657])]),
[iquote('back_demod,448,demod,621,413,657,401,677,657,flip.1')] ).
cnf(4288,plain,
sdtasdt0(xn,sdtpldt0(xm,sdtpldt0(xm,xn))) = sdtasdt0(xn,xn),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[660,18,71,70]),621,707,677])]),
[iquote('hyper,660,18,71,70,demod,621,707,677,flip.1')] ).
cnf(4901,plain,
sdtasdt0(xn,xn) != sz00,
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[601,56]),71,28,68,28])]),
[iquote('para_from,600.1.1,56.4.1,unit_del,71,28,68,28,flip.1')] ).
cnf(4931,plain,
sdtpldt0(xm,xn) = xm,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[442,52,70,660]),27]),
[iquote('hyper,442,52,70,660,unit_del,27')] ).
cnf(4934,plain,
sdtasdt0(xn,xn) = sz00,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4288]),4931,314,665])]),
[iquote('back_demod,4288,demod,4931,314,665,flip.1')] ).
cnf(4936,plain,
$false,
inference(binary,[status(thm)],[4934,4901]),
[iquote('binary,4934.1,4901.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM457+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 09:46:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.82/2.03 ----- Otter 3.3f, August 2004 -----
% 1.82/2.03 The process was started by sandbox2 on n008.cluster.edu,
% 1.82/2.03 Wed Jul 27 09:46:38 2022
% 1.82/2.03 The command was "./otter". The process ID is 31536.
% 1.82/2.03
% 1.82/2.03 set(prolog_style_variables).
% 1.82/2.03 set(auto).
% 1.82/2.03 dependent: set(auto1).
% 1.82/2.03 dependent: set(process_input).
% 1.82/2.03 dependent: clear(print_kept).
% 1.82/2.03 dependent: clear(print_new_demod).
% 1.82/2.03 dependent: clear(print_back_demod).
% 1.82/2.03 dependent: clear(print_back_sub).
% 1.82/2.03 dependent: set(control_memory).
% 1.82/2.03 dependent: assign(max_mem, 12000).
% 1.82/2.03 dependent: assign(pick_given_ratio, 4).
% 1.82/2.03 dependent: assign(stats_level, 1).
% 1.82/2.03 dependent: assign(max_seconds, 10800).
% 1.82/2.03 clear(print_given).
% 1.82/2.03
% 1.82/2.03 formula_list(usable).
% 1.82/2.03 all A (A=A).
% 1.82/2.03 all W0 (aNaturalNumber0(W0)->$T).
% 1.82/2.03 aNaturalNumber0(sz00).
% 1.82/2.03 aNaturalNumber0(sz10).
% 1.82/2.03 sz10!=sz00.
% 1.82/2.03 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->aNaturalNumber0(sdtpldt0(W0,W1))).
% 1.82/2.03 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->aNaturalNumber0(sdtasdt0(W0,W1))).
% 1.82/2.03 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->sdtpldt0(W0,W1)=sdtpldt0(W1,W0)).
% 1.82/2.03 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)->sdtpldt0(sdtpldt0(W0,W1),W2)=sdtpldt0(W0,sdtpldt0(W1,W2))).
% 1.82/2.03 all W0 (aNaturalNumber0(W0)->sdtpldt0(W0,sz00)=W0&W0=sdtpldt0(sz00,W0)).
% 1.82/2.03 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->sdtasdt0(W0,W1)=sdtasdt0(W1,W0)).
% 1.82/2.03 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)->sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2))).
% 1.82/2.03 all W0 (aNaturalNumber0(W0)->sdtasdt0(W0,sz10)=W0&W0=sdtasdt0(sz10,W0)).
% 1.82/2.03 all W0 (aNaturalNumber0(W0)->sdtasdt0(W0,sz00)=sz00&sz00=sdtasdt0(sz00,W0)).
% 1.82/2.03 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))).
% 1.82/2.03 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (sdtpldt0(W0,W1)=sdtpldt0(W0,W2)|sdtpldt0(W1,W0)=sdtpldt0(W2,W0)->W1=W2)).
% 1.82/2.03 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))))).
% 1.82/2.03 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtpldt0(W0,W1)=sz00->W0=sz00&W1=sz00)).
% 1.82/2.03 aNaturalNumber0(xm).
% 1.82/2.03 aNaturalNumber0(xn).
% 1.82/2.03 -(sdtasdt0(xm,xn)=sz00->xm=sz00|xn=sz00).
% 1.82/2.03 end_of_list.
% 1.82/2.03
% 1.82/2.03 -------> usable clausifies to:
% 1.82/2.03
% 1.82/2.03 list(usable).
% 1.82/2.03 0 [] A=A.
% 1.82/2.03 0 [] -aNaturalNumber0(W0)|$T.
% 1.82/2.03 0 [] aNaturalNumber0(sz00).
% 1.82/2.03 0 [] aNaturalNumber0(sz10).
% 1.82/2.03 0 [] sz10!=sz00.
% 1.82/2.03 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|aNaturalNumber0(sdtpldt0(W0,W1)).
% 1.82/2.03 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|aNaturalNumber0(sdtasdt0(W0,W1)).
% 1.82/2.03 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtpldt0(W0,W1)=sdtpldt0(W1,W0).
% 1.82/2.03 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtpldt0(sdtpldt0(W0,W1),W2)=sdtpldt0(W0,sdtpldt0(W1,W2)).
% 1.82/2.03 0 [] -aNaturalNumber0(W0)|sdtpldt0(W0,sz00)=W0.
% 1.82/2.03 0 [] -aNaturalNumber0(W0)|W0=sdtpldt0(sz00,W0).
% 1.82/2.03 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtasdt0(W0,W1)=sdtasdt0(W1,W0).
% 1.82/2.03 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2)).
% 1.82/2.03 0 [] -aNaturalNumber0(W0)|sdtasdt0(W0,sz10)=W0.
% 1.82/2.03 0 [] -aNaturalNumber0(W0)|W0=sdtasdt0(sz10,W0).
% 1.82/2.03 0 [] -aNaturalNumber0(W0)|sdtasdt0(W0,sz00)=sz00.
% 1.82/2.03 0 [] -aNaturalNumber0(W0)|sz00=sdtasdt0(sz00,W0).
% 1.82/2.03 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(W0,sdtpldt0(W1,W2))=sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)).
% 1.82/2.03 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(sdtpldt0(W1,W2),W0)=sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)).
% 1.82/2.03 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtpldt0(W0,W1)!=sdtpldt0(W0,W2)|W1=W2.
% 1.82/2.03 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtpldt0(W1,W0)!=sdtpldt0(W2,W0)|W1=W2.
% 1.82/2.03 0 [] -aNaturalNumber0(W0)|W0=sz00| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(W0,W1)!=sdtasdt0(W0,W2)|W1=W2.
% 1.82/2.03 0 [] -aNaturalNumber0(W0)|W0=sz00| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(W1,W0)!=sdtasdt0(W2,W0)|W1=W2.
% 1.82/2.03 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtpldt0(W0,W1)!=sz00|W0=sz00.
% 1.82/2.03 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtpldt0(W0,W1)!=sz00|W1=sz00.
% 1.82/2.03 0 [] aNaturalNumber0(xm).
% 1.82/2.03 0 [] aNaturalNumber0(xn).
% 1.82/2.03 0 [] sdtasdt0(xm,xn)=sz00.
% 1.82/2.03 0 [] xm!=sz00.
% 1.82/2.03 0 [] xn!=sz00.
% 1.82/2.03 end_of_list.
% 1.82/2.03
% 1.82/2.03 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 1.82/2.03
% 1.82/2.03 This ia a non-Horn set with equality. The strategy will be
% 1.82/2.03 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.82/2.03 deletion, with positive clauses in sos and nonpositive
% 1.82/2.03 clauses in usable.
% 1.82/2.03
% 1.82/2.03 dependent: set(knuth_bendix).
% 1.82/2.03 dependent: set(anl_eq).
% 1.82/2.03 dependent: set(para_from).
% 1.82/2.03 dependent: set(para_into).
% 1.82/2.03 dependent: clear(para_from_right).
% 1.82/2.03 dependent: clear(para_into_right).
% 1.82/2.03 dependent: set(para_from_vars).
% 1.82/2.03 dependent: set(eq_units_both_ways).
% 1.82/2.03 dependent: set(dynamic_demod_all).
% 1.82/2.03 dependent: set(dynamic_demod).
% 1.82/2.03 dependent: set(order_eq).
% 1.82/2.03 dependent: set(back_demod).
% 1.82/2.03 dependent: set(lrpo).
% 1.82/2.03 dependent: set(hyper_res).
% 1.82/2.03 dependent: set(unit_deletion).
% 1.82/2.03 dependent: set(factor).
% 1.82/2.03
% 1.82/2.03 ------------> process usable:
% 1.82/2.03 ** KEPT (pick-wt=3): 1 [] sz10!=sz00.
% 1.82/2.03 ** KEPT (pick-wt=8): 2 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|aNaturalNumber0(sdtpldt0(A,B)).
% 1.82/2.03 ** KEPT (pick-wt=8): 3 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|aNaturalNumber0(sdtasdt0(A,B)).
% 1.82/2.03 ** KEPT (pick-wt=11): 4 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtpldt0(A,B)=sdtpldt0(B,A).
% 1.82/2.03 ** KEPT (pick-wt=17): 5 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(sdtpldt0(A,B),C)=sdtpldt0(A,sdtpldt0(B,C)).
% 1.82/2.03 ** KEPT (pick-wt=7): 6 [] -aNaturalNumber0(A)|sdtpldt0(A,sz00)=A.
% 1.82/2.03 ** KEPT (pick-wt=7): 8 [copy,7,flip.2] -aNaturalNumber0(A)|sdtpldt0(sz00,A)=A.
% 1.82/2.03 ** KEPT (pick-wt=11): 9 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtasdt0(A,B)=sdtasdt0(B,A).
% 1.82/2.03 ** KEPT (pick-wt=17): 10 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtasdt0(sdtasdt0(A,B),C)=sdtasdt0(A,sdtasdt0(B,C)).
% 1.82/2.03 ** KEPT (pick-wt=7): 11 [] -aNaturalNumber0(A)|sdtasdt0(A,sz10)=A.
% 1.82/2.03 ** KEPT (pick-wt=7): 13 [copy,12,flip.2] -aNaturalNumber0(A)|sdtasdt0(sz10,A)=A.
% 1.82/2.03 ** KEPT (pick-wt=7): 14 [] -aNaturalNumber0(A)|sdtasdt0(A,sz00)=sz00.
% 1.82/2.03 ** KEPT (pick-wt=7): 16 [copy,15,flip.2] -aNaturalNumber0(A)|sdtasdt0(sz00,A)=sz00.
% 1.82/2.03 ** 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)).
% 1.82/2.03 ** 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).
% 1.82/2.03 ** KEPT (pick-wt=16): 21 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(A,B)!=sdtpldt0(A,C)|B=C.
% 1.82/2.03 ** KEPT (pick-wt=16): 22 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(B,A)!=sdtpldt0(C,A)|B=C.
% 1.82/2.03 ** KEPT (pick-wt=19): 23 [] -aNaturalNumber0(A)|A=sz00| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtasdt0(A,B)!=sdtasdt0(A,C)|B=C.
% 1.82/2.03 ** KEPT (pick-wt=19): 24 [] -aNaturalNumber0(A)|A=sz00| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtasdt0(B,A)!=sdtasdt0(C,A)|B=C.
% 1.82/2.03 ** KEPT (pick-wt=12): 25 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtpldt0(A,B)!=sz00|A=sz00.
% 1.82/2.03 ** KEPT (pick-wt=12): 26 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtpldt0(A,B)!=sz00|B=sz00.
% 1.82/2.03 ** KEPT (pick-wt=3): 27 [] xm!=sz00.
% 1.82/2.03 ** KEPT (pick-wt=3): 28 [] xn!=sz00.
% 1.82/2.03
% 1.82/2.03 ------------> process sos:
% 1.82/2.03 ** KEPT (pick-wt=3): 67 [] A=A.
% 1.82/2.03 ** KEPT (pick-wt=2): 68 [] aNaturalNumber0(sz00).
% 1.82/2.03 ** KEPT (pick-wt=2): 69 [] aNaturalNumber0(sz10).
% 1.82/2.03 ** KEPT (pick-wt=2): 70 [] aNaturalNumber0(xm).
% 1.82/2.03 ** KEPT (pick-wt=2): 71 [] aNaturalNumber0(xn).
% 1.82/2.03 ** KEPT (pick-wt=5): 72 [] sdtasdt0(xm,xn)=sz00.
% 1.82/2.03 ---> New Demodulator: 73 [new_demod,72] sdtasdt0(xm,xn)=sz00.
% 1.82/2.03 Following clause subsumed by 67 during input processing: 0 [copy,67,flip.1] A=A.
% 1.82/2.03 67 back subsumes 66.
% 1.82/2.03 67 back subsumes 65.
% 1.82/2.03 67 back subsumes 64.
% 1.82/2.03 67 back subsumes 58.
% 1.82/2.03 67 back subsumes 54.
% 1.82/2.03 67 back subsumes 50.
% 1.82/2.03 67 back subsumes 47.
% 1.82/2.03 67 back subsumes 35.
% 1.82/2.03 67 back subsumes 31.
% 1.82/2.03 >>>> Starting back demodulation with 73.
% 1.82/2.03
% 1.82/2.03 ======= end of input processing =======
% 15.32/15.53
% 15.32/15.53 =========== start of search ===========
% 15.32/15.53
% 15.32/15.53
% 15.32/15.53 Resetting weight limit to 9.
% 15.32/15.53
% 15.32/15.53
% 15.32/15.53 Resetting weight limit to 9.
% 15.32/15.53
% 15.32/15.53 sos_size=1553
% 15.32/15.53
% 15.32/15.53
% 15.32/15.53 Resetting weight limit to 8.
% 15.32/15.53
% 15.32/15.53
% 15.32/15.53 Resetting weight limit to 8.
% 15.32/15.53
% 15.32/15.53 sos_size=1557
% 15.32/15.53
% 15.32/15.53 -- HEY sandbox2, WE HAVE A PROOF!! --
% 15.32/15.53
% 15.32/15.53 ----> UNIT CONFLICT at 13.50 sec ----> 4936 [binary,4934.1,4901.1] $F.
% 15.32/15.53
% 15.32/15.53 Length of proof is 39. Level of proof is 8.
% 15.32/15.53
% 15.32/15.53 ---------------- PROOF ----------------
% 15.32/15.53 % SZS status Theorem
% 15.32/15.53 % SZS output start Refutation
% See solution above
% 15.32/15.53 ------------ end of proof -------------
% 15.32/15.53
% 15.32/15.53
% 15.32/15.53 Search stopped by max_proofs option.
% 15.32/15.53
% 15.32/15.53
% 15.32/15.53 Search stopped by max_proofs option.
% 15.32/15.53
% 15.32/15.53 ============ end of search ============
% 15.32/15.53
% 15.32/15.53 -------------- statistics -------------
% 15.32/15.53 clauses given 165
% 15.32/15.53 clauses generated 1411443
% 15.32/15.53 clauses kept 2633
% 15.32/15.53 clauses forward subsumed 13801
% 15.32/15.53 clauses back subsumed 13
% 15.32/15.53 Kbytes malloced 4882
% 15.32/15.53
% 15.32/15.53 ----------- times (seconds) -----------
% 15.32/15.53 user CPU time 13.50 (0 hr, 0 min, 13 sec)
% 15.32/15.53 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 15.32/15.53 wall-clock time 15 (0 hr, 0 min, 15 sec)
% 15.32/15.53
% 15.32/15.53 That finishes the proof of the theorem.
% 15.32/15.53
% 15.32/15.53 Process 31536 finished Wed Jul 27 09:46:53 2022
% 15.32/15.53 Otter interrupted
% 15.32/15.53 PROOF FOUND
%------------------------------------------------------------------------------