TSTP Solution File: NUM467+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM467+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 13:08:28 EDT 2022
% Result : Theorem 206.05s 206.22s
% Output : Refutation 206.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of clauses : 16 ( 11 unt; 0 nHn; 15 RR)
% Number of literals : 26 ( 10 equ; 12 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| aNaturalNumber0(sdtpldt0(A,B)) ),
file('NUM467+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(C)
| sdtasdt0(A,sdtpldt0(B,C)) = sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) ),
file('NUM467+2.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(55,axiom,
( ~ aNaturalNumber0(A)
| sdtpldt0(xm,xn) != sdtasdt0(xl,A) ),
file('NUM467+2.p',unknown),
[] ).
cnf(131,axiom,
A = A,
file('NUM467+2.p',unknown),
[] ).
cnf(134,axiom,
aNaturalNumber0(xl),
file('NUM467+2.p',unknown),
[] ).
cnf(137,axiom,
aNaturalNumber0(dollar_c1),
file('NUM467+2.p',unknown),
[] ).
cnf(138,axiom,
xm = sdtasdt0(xl,dollar_c1),
file('NUM467+2.p',unknown),
[] ).
cnf(140,plain,
sdtasdt0(xl,dollar_c1) = xm,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[138])]),
[iquote('copy,138,flip.1')] ).
cnf(142,axiom,
aNaturalNumber0(dollar_c2),
file('NUM467+2.p',unknown),
[] ).
cnf(143,axiom,
xn = sdtasdt0(xl,dollar_c2),
file('NUM467+2.p',unknown),
[] ).
cnf(145,plain,
sdtasdt0(xl,dollar_c2) = xn,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[143])]),
[iquote('copy,143,flip.1')] ).
cnf(3673,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(dollar_c1,dollar_c2)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[142,18,134,137]),140,145]),
[iquote('hyper,142,18,134,137,demod,140,145')] ).
cnf(4146,plain,
aNaturalNumber0(sdtpldt0(dollar_c1,dollar_c2)),
inference(hyper,[status(thm)],[142,2,137]),
[iquote('hyper,142,2,137')] ).
cnf(4316,plain,
( ~ aNaturalNumber0(A)
| sdtasdt0(xl,sdtpldt0(dollar_c1,dollar_c2)) != sdtasdt0(xl,A) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[55]),3673]),
[iquote('back_demod,55,demod,3673')] ).
cnf(5991,plain,
$false,
inference(hyper,[status(thm)],[4316,4146,131]),
[iquote('hyper,4316,4146,131')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM467+2 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 10:15:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.33/2.50 ----- Otter 3.3f, August 2004 -----
% 2.33/2.50 The process was started by sandbox on n023.cluster.edu,
% 2.33/2.50 Wed Jul 27 10:15:18 2022
% 2.33/2.50 The command was "./otter". The process ID is 30013.
% 2.33/2.50
% 2.33/2.50 set(prolog_style_variables).
% 2.33/2.50 set(auto).
% 2.33/2.50 dependent: set(auto1).
% 2.33/2.50 dependent: set(process_input).
% 2.33/2.50 dependent: clear(print_kept).
% 2.33/2.50 dependent: clear(print_new_demod).
% 2.33/2.50 dependent: clear(print_back_demod).
% 2.33/2.50 dependent: clear(print_back_sub).
% 2.33/2.50 dependent: set(control_memory).
% 2.33/2.50 dependent: assign(max_mem, 12000).
% 2.33/2.50 dependent: assign(pick_given_ratio, 4).
% 2.33/2.50 dependent: assign(stats_level, 1).
% 2.33/2.50 dependent: assign(max_seconds, 10800).
% 2.33/2.50 clear(print_given).
% 2.33/2.50
% 2.33/2.50 formula_list(usable).
% 2.33/2.50 all A (A=A).
% 2.33/2.50 all W0 (aNaturalNumber0(W0)->$T).
% 2.33/2.50 aNaturalNumber0(sz00).
% 2.33/2.50 aNaturalNumber0(sz10).
% 2.33/2.50 sz10!=sz00.
% 2.33/2.50 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->aNaturalNumber0(sdtpldt0(W0,W1))).
% 2.33/2.50 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->aNaturalNumber0(sdtasdt0(W0,W1))).
% 2.33/2.50 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->sdtpldt0(W0,W1)=sdtpldt0(W1,W0)).
% 2.33/2.50 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)->sdtpldt0(sdtpldt0(W0,W1),W2)=sdtpldt0(W0,sdtpldt0(W1,W2))).
% 2.33/2.50 all W0 (aNaturalNumber0(W0)->sdtpldt0(W0,sz00)=W0&W0=sdtpldt0(sz00,W0)).
% 2.33/2.50 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->sdtasdt0(W0,W1)=sdtasdt0(W1,W0)).
% 2.33/2.50 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)->sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2))).
% 2.33/2.50 all W0 (aNaturalNumber0(W0)->sdtasdt0(W0,sz10)=W0&W0=sdtasdt0(sz10,W0)).
% 2.33/2.50 all W0 (aNaturalNumber0(W0)->sdtasdt0(W0,sz00)=sz00&sz00=sdtasdt0(sz00,W0)).
% 2.33/2.50 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))).
% 2.33/2.50 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (sdtpldt0(W0,W1)=sdtpldt0(W0,W2)|sdtpldt0(W1,W0)=sdtpldt0(W2,W0)->W1=W2)).
% 2.33/2.50 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))))).
% 2.33/2.50 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtpldt0(W0,W1)=sz00->W0=sz00&W1=sz00)).
% 2.33/2.50 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtasdt0(W0,W1)=sz00->W0=sz00|W1=sz00)).
% 2.33/2.50 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtlse_qdt0(W0,W1)<-> (exists W2 (aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1)))).
% 2.33/2.50 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtlse_qdt0(W0,W1)-> (all W2 (W2=sdtmndt0(W1,W0)<->aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1)))).
% 2.33/2.50 all W0 (aNaturalNumber0(W0)->sdtlse_qdt0(W0,W0)).
% 2.33/2.50 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtlse_qdt0(W0,W1)&sdtlse_qdt0(W1,W0)->W0=W1)).
% 2.33/2.50 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (sdtlse_qdt0(W0,W1)&sdtlse_qdt0(W1,W2)->sdtlse_qdt0(W0,W2))).
% 2.33/2.50 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->sdtlse_qdt0(W0,W1)|W1!=W0&sdtlse_qdt0(W1,W0)).
% 2.33/2.50 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)))))).
% 2.33/2.50 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)))).
% 2.33/2.50 all W0 (aNaturalNumber0(W0)->W0=sz00|W0=sz10|sz10!=W0&sdtlse_qdt0(sz10,W0)).
% 2.33/2.50 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (W0!=sz00->sdtlse_qdt0(W1,sdtasdt0(W1,W0)))).
% 2.33/2.50 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (iLess0(W0,W1)->$T)).
% 2.33/2.50 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (W0!=W1&sdtlse_qdt0(W0,W1)->iLess0(W0,W1))).
% 2.33/2.50 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (doDivides0(W0,W1)<-> (exists W2 (aNaturalNumber0(W2)&W1=sdtasdt0(W0,W2))))).
% 2.33/2.50 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (W0!=sz00&doDivides0(W0,W1)-> (all W2 (W2=sdtsldt0(W1,W0)<->aNaturalNumber0(W2)&W1=sdtasdt0(W0,W2))))).
% 2.33/2.50 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (doDivides0(W0,W1)&doDivides0(W1,W2)->doDivides0(W0,W2))).
% 2.33/2.50 aNaturalNumber0(xl).
% 2.33/2.50 aNaturalNumber0(xm).
% 2.33/2.50 aNaturalNumber0(xn).
% 2.33/2.50 exists W0 (aNaturalNumber0(W0)&xm=sdtasdt0(xl,W0)).
% 2.33/2.50 doDivides0(xl,xm).
% 2.33/2.50 exists W0 (aNaturalNumber0(W0)&xn=sdtasdt0(xl,W0)).
% 2.33/2.50 doDivides0(xl,xn).
% 2.33/2.50 -((exists W0 (aNaturalNumber0(W0)&sdtpldt0(xm,xn)=sdtasdt0(xl,W0)))|doDivides0(xl,sdtpldt0(xm,xn))).
% 2.33/2.50 end_of_list.
% 2.33/2.50
% 2.33/2.50 -------> usable clausifies to:
% 2.33/2.50
% 2.33/2.50 list(usable).
% 2.33/2.50 0 [] A=A.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)|$T.
% 2.33/2.50 0 [] aNaturalNumber0(sz00).
% 2.33/2.50 0 [] aNaturalNumber0(sz10).
% 2.33/2.50 0 [] sz10!=sz00.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|aNaturalNumber0(sdtpldt0(W0,W1)).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|aNaturalNumber0(sdtasdt0(W0,W1)).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtpldt0(W0,W1)=sdtpldt0(W1,W0).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtpldt0(sdtpldt0(W0,W1),W2)=sdtpldt0(W0,sdtpldt0(W1,W2)).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)|sdtpldt0(W0,sz00)=W0.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)|W0=sdtpldt0(sz00,W0).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtasdt0(W0,W1)=sdtasdt0(W1,W0).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2)).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)|sdtasdt0(W0,sz10)=W0.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)|W0=sdtasdt0(sz10,W0).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)|sdtasdt0(W0,sz00)=sz00.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)|sz00=sdtasdt0(sz00,W0).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(W0,sdtpldt0(W1,W2))=sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(sdtpldt0(W1,W2),W0)=sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtpldt0(W0,W1)!=sdtpldt0(W0,W2)|W1=W2.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtpldt0(W1,W0)!=sdtpldt0(W2,W0)|W1=W2.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)|W0=sz00| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(W0,W1)!=sdtasdt0(W0,W2)|W1=W2.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)|W0=sz00| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(W1,W0)!=sdtasdt0(W2,W0)|W1=W2.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtpldt0(W0,W1)!=sz00|W0=sz00.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtpldt0(W0,W1)!=sz00|W1=sz00.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtasdt0(W0,W1)!=sz00|W0=sz00|W1=sz00.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|aNaturalNumber0($f1(W0,W1)).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|sdtpldt0(W0,$f1(W0,W1))=W1.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtpldt0(W0,W2)!=W1.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|W2!=sdtmndt0(W1,W0)|aNaturalNumber0(W2).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|W2!=sdtmndt0(W1,W0)|sdtpldt0(W0,W2)=W1.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|W2=sdtmndt0(W1,W0)| -aNaturalNumber0(W2)|sdtpldt0(W0,W2)!=W1.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)|sdtlse_qdt0(W0,W0).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)| -sdtlse_qdt0(W1,W0)|W0=W1.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)| -sdtlse_qdt0(W0,W1)| -sdtlse_qdt0(W1,W2)|sdtlse_qdt0(W0,W2).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtlse_qdt0(W0,W1)|W1!=W0.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtlse_qdt0(W0,W1)|sdtlse_qdt0(W1,W0).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtpldt0(W2,W0)!=sdtpldt0(W2,W1).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtlse_qdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1)).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtpldt0(W0,W2)!=sdtpldt0(W1,W2).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtlse_qdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtasdt0(W0,W1)!=sdtasdt0(W0,W2).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtlse_qdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtasdt0(W1,W0)!=sdtasdt0(W2,W0).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtlse_qdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)|W0=sz00|W0=sz10|sz10!=W0.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)|W0=sz00|W0=sz10|sdtlse_qdt0(sz10,W0).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=sz00|sdtlse_qdt0(W1,sdtasdt0(W1,W0)).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -iLess0(W0,W1)|$T.
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)|iLess0(W0,W1).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -doDivides0(W0,W1)|aNaturalNumber0($f2(W0,W1)).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -doDivides0(W0,W1)|W1=sdtasdt0(W0,$f2(W0,W1)).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|doDivides0(W0,W1)| -aNaturalNumber0(W2)|W1!=sdtasdt0(W0,W2).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=sz00| -doDivides0(W0,W1)|W2!=sdtsldt0(W1,W0)|aNaturalNumber0(W2).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=sz00| -doDivides0(W0,W1)|W2!=sdtsldt0(W1,W0)|W1=sdtasdt0(W0,W2).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=sz00| -doDivides0(W0,W1)|W2=sdtsldt0(W1,W0)| -aNaturalNumber0(W2)|W1!=sdtasdt0(W0,W2).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)| -doDivides0(W0,W1)| -doDivides0(W1,W2)|doDivides0(W0,W2).
% 2.33/2.50 0 [] aNaturalNumber0(xl).
% 2.33/2.50 0 [] aNaturalNumber0(xm).
% 2.33/2.50 0 [] aNaturalNumber0(xn).
% 2.33/2.50 0 [] aNaturalNumber0($c1).
% 2.33/2.50 0 [] xm=sdtasdt0(xl,$c1).
% 2.33/2.50 0 [] doDivides0(xl,xm).
% 2.33/2.50 0 [] aNaturalNumber0($c2).
% 2.33/2.50 0 [] xn=sdtasdt0(xl,$c2).
% 2.33/2.50 0 [] doDivides0(xl,xn).
% 2.33/2.50 0 [] -aNaturalNumber0(W0)|sdtpldt0(xm,xn)!=sdtasdt0(xl,W0).
% 2.33/2.50 0 [] -doDivides0(xl,sdtpldt0(xm,xn)).
% 2.33/2.50 end_of_list.
% 2.33/2.50
% 2.33/2.50 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 2.33/2.50
% 2.33/2.50 This ia a non-Horn set with equality. The strategy will be
% 2.33/2.50 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.33/2.50 deletion, with positive clauses in sos and nonpositive
% 2.33/2.50 clauses in usable.
% 2.33/2.50
% 2.33/2.50 dependent: set(knuth_bendix).
% 2.33/2.50 dependent: set(anl_eq).
% 2.33/2.50 dependent: set(para_from).
% 2.33/2.50 dependent: set(para_into).
% 2.33/2.50 dependent: clear(para_from_right).
% 2.33/2.50 dependent: clear(para_into_right).
% 2.33/2.50 dependent: set(para_from_vars).
% 2.33/2.50 dependent: set(eq_units_both_ways).
% 2.33/2.50 dependent: set(dynamic_demod_all).
% 2.33/2.50 dependent: set(dynamic_demod).
% 2.33/2.50 dependent: set(order_eq).
% 2.33/2.50 dependent: set(back_demod).
% 2.33/2.50 dependent: set(lrpo).
% 2.33/2.50 dependent: set(hyper_res).
% 2.33/2.50 dependent: set(unit_deletion).
% 2.33/2.50 dependent: set(factor).
% 2.33/2.50
% 2.33/2.50 ------------> process usable:
% 2.33/2.50 ** KEPT (pick-wt=3): 1 [] sz10!=sz00.
% 2.33/2.50 ** KEPT (pick-wt=8): 2 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|aNaturalNumber0(sdtpldt0(A,B)).
% 2.33/2.50 ** KEPT (pick-wt=8): 3 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|aNaturalNumber0(sdtasdt0(A,B)).
% 2.33/2.50 ** KEPT (pick-wt=11): 4 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtpldt0(A,B)=sdtpldt0(B,A).
% 2.33/2.50 ** KEPT (pick-wt=17): 5 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(sdtpldt0(A,B),C)=sdtpldt0(A,sdtpldt0(B,C)).
% 2.33/2.50 ** KEPT (pick-wt=7): 6 [] -aNaturalNumber0(A)|sdtpldt0(A,sz00)=A.
% 2.33/2.50 ** KEPT (pick-wt=7): 8 [copy,7,flip.2] -aNaturalNumber0(A)|sdtpldt0(sz00,A)=A.
% 2.33/2.50 ** KEPT (pick-wt=11): 9 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtasdt0(A,B)=sdtasdt0(B,A).
% 2.33/2.50 ** KEPT (pick-wt=17): 10 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtasdt0(sdtasdt0(A,B),C)=sdtasdt0(A,sdtasdt0(B,C)).
% 2.33/2.50 ** KEPT (pick-wt=7): 11 [] -aNaturalNumber0(A)|sdtasdt0(A,sz10)=A.
% 2.33/2.50 ** KEPT (pick-wt=7): 13 [copy,12,flip.2] -aNaturalNumber0(A)|sdtasdt0(sz10,A)=A.
% 2.33/2.50 ** KEPT (pick-wt=7): 14 [] -aNaturalNumber0(A)|sdtasdt0(A,sz00)=sz00.
% 2.33/2.50 ** KEPT (pick-wt=7): 16 [copy,15,flip.2] -aNaturalNumber0(A)|sdtasdt0(sz00,A)=sz00.
% 2.33/2.52 ** 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)).
% 2.33/2.52 ** 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).
% 2.33/2.52 ** KEPT (pick-wt=16): 21 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(A,B)!=sdtpldt0(A,C)|B=C.
% 2.33/2.52 ** KEPT (pick-wt=16): 22 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(B,A)!=sdtpldt0(C,A)|B=C.
% 2.33/2.52 ** KEPT (pick-wt=19): 23 [] -aNaturalNumber0(A)|A=sz00| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtasdt0(A,B)!=sdtasdt0(A,C)|B=C.
% 2.33/2.52 ** KEPT (pick-wt=19): 24 [] -aNaturalNumber0(A)|A=sz00| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtasdt0(B,A)!=sdtasdt0(C,A)|B=C.
% 2.33/2.52 ** KEPT (pick-wt=12): 25 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtpldt0(A,B)!=sz00|A=sz00.
% 2.33/2.52 ** KEPT (pick-wt=12): 26 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtpldt0(A,B)!=sz00|B=sz00.
% 2.33/2.52 ** KEPT (pick-wt=15): 27 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtasdt0(A,B)!=sz00|A=sz00|B=sz00.
% 2.33/2.52 ** KEPT (pick-wt=11): 28 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|aNaturalNumber0($f1(A,B)).
% 2.33/2.52 ** KEPT (pick-wt=14): 29 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|sdtpldt0(A,$f1(A,B))=B.
% 2.33/2.52 ** KEPT (pick-wt=14): 30 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtpldt0(A,C)!=B.
% 2.33/2.52 ** KEPT (pick-wt=14): 31 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|C!=sdtmndt0(B,A)|aNaturalNumber0(C).
% 2.33/2.52 ** KEPT (pick-wt=17): 32 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|C!=sdtmndt0(B,A)|sdtpldt0(A,C)=B.
% 2.33/2.52 ** KEPT (pick-wt=19): 33 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|C=sdtmndt0(B,A)| -aNaturalNumber0(C)|sdtpldt0(A,C)!=B.
% 2.33/2.52 ** KEPT (pick-wt=5): 34 [] -aNaturalNumber0(A)|sdtlse_qdt0(A,A).
% 2.33/2.52 ** KEPT (pick-wt=13): 35 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)| -sdtlse_qdt0(B,A)|A=B.
% 2.33/2.52 ** KEPT (pick-wt=15): 36 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)| -sdtlse_qdt0(A,B)| -sdtlse_qdt0(B,C)|sdtlse_qdt0(A,C).
% 2.33/2.52 ** KEPT (pick-wt=10): 37 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtlse_qdt0(A,B)|B!=A.
% 2.33/2.52 ** KEPT (pick-wt=10): 38 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtlse_qdt0(A,B)|sdtlse_qdt0(B,A).
% 2.33/2.52 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).
% 2.33/2.52 ** 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)).
% 2.33/2.52 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).
% 2.33/2.52 ** 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)).
% 2.33/2.52 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).
% 2.33/2.52 ** 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)).
% 2.33/2.52 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).
% 2.33/2.52 ** 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)).
% 2.33/2.52 ** KEPT (pick-wt=11): 43 [] -aNaturalNumber0(A)|A=sz00|A=sz10|sz10!=A.
% 2.33/2.52 ** KEPT (pick-wt=11): 44 [] -aNaturalNumber0(A)|A=sz00|A=sz10|sdtlse_qdt0(sz10,A).
% 2.33/2.52 ** KEPT (pick-wt=12): 45 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=sz00|sdtlse_qdt0(B,sdtasdt0(B,A)).
% 206.05/206.22 ** KEPT (pick-wt=13): 46 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=B| -sdtlse_qdt0(A,B)|iLess0(A,B).
% 206.05/206.22 ** KEPT (pick-wt=11): 47 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -doDivides0(A,B)|aNaturalNumber0($f2(A,B)).
% 206.05/206.22 ** KEPT (pick-wt=14): 49 [copy,48,flip.4] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -doDivides0(A,B)|sdtasdt0(A,$f2(A,B))=B.
% 206.05/206.22 ** KEPT (pick-wt=14): 50 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|doDivides0(A,B)| -aNaturalNumber0(C)|B!=sdtasdt0(A,C).
% 206.05/206.22 ** KEPT (pick-wt=17): 51 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=sz00| -doDivides0(A,B)|C!=sdtsldt0(B,A)|aNaturalNumber0(C).
% 206.05/206.22 ** KEPT (pick-wt=20): 52 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=sz00| -doDivides0(A,B)|C!=sdtsldt0(B,A)|B=sdtasdt0(A,C).
% 206.05/206.22 ** KEPT (pick-wt=22): 53 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=sz00| -doDivides0(A,B)|C=sdtsldt0(B,A)| -aNaturalNumber0(C)|B!=sdtasdt0(A,C).
% 206.05/206.22 ** KEPT (pick-wt=15): 54 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)| -doDivides0(A,B)| -doDivides0(B,C)|doDivides0(A,C).
% 206.05/206.22 ** KEPT (pick-wt=9): 55 [] -aNaturalNumber0(A)|sdtpldt0(xm,xn)!=sdtasdt0(xl,A).
% 206.05/206.22 ** KEPT (pick-wt=5): 56 [] -doDivides0(xl,sdtpldt0(xm,xn)).
% 206.05/206.22
% 206.05/206.22 ------------> process sos:
% 206.05/206.22 ** KEPT (pick-wt=3): 131 [] A=A.
% 206.05/206.22 ** KEPT (pick-wt=2): 132 [] aNaturalNumber0(sz00).
% 206.05/206.22 ** KEPT (pick-wt=2): 133 [] aNaturalNumber0(sz10).
% 206.05/206.22 ** KEPT (pick-wt=2): 134 [] aNaturalNumber0(xl).
% 206.05/206.22 ** KEPT (pick-wt=2): 135 [] aNaturalNumber0(xm).
% 206.05/206.22 ** KEPT (pick-wt=2): 136 [] aNaturalNumber0(xn).
% 206.05/206.22 ** KEPT (pick-wt=2): 137 [] aNaturalNumber0($c1).
% 206.05/206.22 ** KEPT (pick-wt=5): 139 [copy,138,flip.1] sdtasdt0(xl,$c1)=xm.
% 206.05/206.22 ---> New Demodulator: 140 [new_demod,139] sdtasdt0(xl,$c1)=xm.
% 206.05/206.22 ** KEPT (pick-wt=3): 141 [] doDivides0(xl,xm).
% 206.05/206.22 ** KEPT (pick-wt=2): 142 [] aNaturalNumber0($c2).
% 206.05/206.22 ** KEPT (pick-wt=5): 144 [copy,143,flip.1] sdtasdt0(xl,$c2)=xn.
% 206.05/206.22 ---> New Demodulator: 145 [new_demod,144] sdtasdt0(xl,$c2)=xn.
% 206.05/206.22 ** KEPT (pick-wt=3): 146 [] doDivides0(xl,xn).
% 206.05/206.22 Following clause subsumed by 131 during input processing: 0 [copy,131,flip.1] A=A.
% 206.05/206.22 131 back subsumes 127.
% 206.05/206.22 131 back subsumes 126.
% 206.05/206.22 131 back subsumes 125.
% 206.05/206.22 131 back subsumes 98.
% 206.05/206.22 131 back subsumes 86.
% 206.05/206.22 131 back subsumes 82.
% 206.05/206.22 131 back subsumes 78.
% 206.05/206.22 131 back subsumes 75.
% 206.05/206.22 131 back subsumes 63.
% 206.05/206.22 131 back subsumes 59.
% 206.05/206.22 >>>> Starting back demodulation with 140.
% 206.05/206.22 >>>> Starting back demodulation with 145.
% 206.05/206.22
% 206.05/206.22 ======= end of input processing =======
% 206.05/206.22
% 206.05/206.22 =========== start of search ===========
% 206.05/206.22
% 206.05/206.22
% 206.05/206.22 Resetting weight limit to 6.
% 206.05/206.22
% 206.05/206.22
% 206.05/206.22 Resetting weight limit to 6.
% 206.05/206.22
% 206.05/206.22 sos_size=1425
% 206.05/206.22
% 206.05/206.22
% 206.05/206.22 Resetting weight limit to 5.
% 206.05/206.22
% 206.05/206.22
% 206.05/206.22 Resetting weight limit to 5.
% 206.05/206.22
% 206.05/206.22 sos_size=1489
% 206.05/206.22
% 206.05/206.22 -- HEY sandbox, WE HAVE A PROOF!! --
% 206.05/206.22
% 206.05/206.22 -----> EMPTY CLAUSE at 203.68 sec ----> 5991 [hyper,4316,4146,131] $F.
% 206.05/206.22
% 206.05/206.22 Length of proof is 6. Level of proof is 3.
% 206.05/206.22
% 206.05/206.22 ---------------- PROOF ----------------
% 206.05/206.22 % SZS status Theorem
% 206.05/206.22 % SZS output start Refutation
% See solution above
% 206.05/206.22 ------------ end of proof -------------
% 206.05/206.22
% 206.05/206.22
% 206.05/206.22 Search stopped by max_proofs option.
% 206.05/206.22
% 206.05/206.22
% 206.05/206.22 Search stopped by max_proofs option.
% 206.05/206.22
% 206.05/206.22 ============ end of search ============
% 206.05/206.22
% 206.05/206.22 -------------- statistics -------------
% 206.05/206.22 clauses given 927
% 206.05/206.22 clauses generated 16370140
% 206.05/206.22 clauses kept 3556
% 206.05/206.22 clauses forward subsumed 13731
% 206.05/206.22 clauses back subsumed 135
% 206.05/206.22 Kbytes malloced 5859
% 206.05/206.22
% 206.05/206.22 ----------- times (seconds) -----------
% 206.05/206.22 user CPU time 203.68 (0 hr, 3 min, 23 sec)
% 206.05/206.22 system CPU time 0.02 (0 hr, 0 min, 0 sec)
% 206.05/206.22 wall-clock time 206 (0 hr, 3 min, 26 sec)
% 206.05/206.22
% 206.05/206.22 That finishes the proof of the theorem.
% 206.05/206.22
% 206.05/206.22 Process 30013 finished Wed Jul 27 10:18:44 2022
% 206.05/206.22 Otter interrupted
% 206.05/206.22 PROOF FOUND
%------------------------------------------------------------------------------