TSTP Solution File: COM023+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COM023+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.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 12:48:24 EDT 2022
% Result : Theorem 3.49s 3.68s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of clauses : 21 ( 12 unt; 5 nHn; 21 RR)
% Number of literals : 50 ( 0 equ; 25 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(15,axiom,
( ~ aRewritingSystem0(A)
| isConfluent0(A)
| aElement0(dollar_f5(A)) ),
file('COM023+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ aRewritingSystem0(A)
| isConfluent0(A)
| aElement0(dollar_f4(A)) ),
file('COM023+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ aRewritingSystem0(A)
| isConfluent0(A)
| aElement0(dollar_f3(A)) ),
file('COM023+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ aRewritingSystem0(A)
| isConfluent0(A)
| sdtmndtasgtdt0(dollar_f5(A),A,dollar_f4(A)) ),
file('COM023+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ aRewritingSystem0(A)
| isConfluent0(A)
| sdtmndtasgtdt0(dollar_f5(A),A,dollar_f3(A)) ),
file('COM023+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ aRewritingSystem0(A)
| isConfluent0(A)
| ~ aElement0(B)
| ~ sdtmndtasgtdt0(dollar_f4(A),A,B)
| ~ sdtmndtasgtdt0(dollar_f3(A),A,B) ),
file('COM023+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ aElement0(A)
| ~ aElement0(B)
| ~ aElement0(C)
| ~ sdtmndtasgtdt0(A,xR,B)
| ~ sdtmndtasgtdt0(A,xR,C)
| aElement0(dollar_f14(A,B,C)) ),
file('COM023+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ aElement0(A)
| ~ aElement0(B)
| ~ aElement0(C)
| ~ sdtmndtasgtdt0(A,xR,B)
| ~ sdtmndtasgtdt0(A,xR,C)
| sdtmndtasgtdt0(B,xR,dollar_f14(A,B,C)) ),
file('COM023+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ aElement0(A)
| ~ aElement0(B)
| ~ aElement0(C)
| ~ sdtmndtasgtdt0(A,xR,B)
| ~ sdtmndtasgtdt0(A,xR,C)
| sdtmndtasgtdt0(C,xR,dollar_f14(A,B,C)) ),
file('COM023+1.p',unknown),
[] ).
cnf(43,axiom,
~ isConfluent0(xR),
file('COM023+1.p',unknown),
[] ).
cnf(87,axiom,
aRewritingSystem0(xR),
file('COM023+1.p',unknown),
[] ).
cnf(90,plain,
sdtmndtasgtdt0(dollar_f5(xR),xR,dollar_f3(xR)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[87,19]),43]),
[iquote('hyper,87,19,unit_del,43')] ).
cnf(91,plain,
sdtmndtasgtdt0(dollar_f5(xR),xR,dollar_f4(xR)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[87,18]),43]),
[iquote('hyper,87,18,unit_del,43')] ).
cnf(92,plain,
aElement0(dollar_f3(xR)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[87,17]),43]),
[iquote('hyper,87,17,unit_del,43')] ).
cnf(93,plain,
aElement0(dollar_f4(xR)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[87,16]),43]),
[iquote('hyper,87,16,unit_del,43')] ).
cnf(94,plain,
aElement0(dollar_f5(xR)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[87,15]),43]),
[iquote('hyper,87,15,unit_del,43')] ).
cnf(118,plain,
sdtmndtasgtdt0(dollar_f4(xR),xR,dollar_f14(dollar_f5(xR),dollar_f3(xR),dollar_f4(xR))),
inference(hyper,[status(thm)],[91,42,94,92,93,90]),
[iquote('hyper,91,42,94,92,93,90')] ).
cnf(120,plain,
sdtmndtasgtdt0(dollar_f3(xR),xR,dollar_f14(dollar_f5(xR),dollar_f3(xR),dollar_f4(xR))),
inference(hyper,[status(thm)],[91,41,94,92,93,90]),
[iquote('hyper,91,41,94,92,93,90')] ).
cnf(122,plain,
aElement0(dollar_f14(dollar_f5(xR),dollar_f3(xR),dollar_f4(xR))),
inference(hyper,[status(thm)],[91,40,94,92,93,90]),
[iquote('hyper,91,40,94,92,93,90')] ).
cnf(1022,plain,
isConfluent0(xR),
inference(hyper,[status(thm)],[120,20,87,122,118]),
[iquote('hyper,120,20,87,122,118')] ).
cnf(1023,plain,
$false,
inference(binary,[status(thm)],[1022,43]),
[iquote('binary,1022.1,43.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM023+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 06:45:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.85/2.05 ----- Otter 3.3f, August 2004 -----
% 1.85/2.05 The process was started by sandbox on n029.cluster.edu,
% 1.85/2.05 Wed Jul 27 06:45:14 2022
% 1.85/2.05 The command was "./otter". The process ID is 4469.
% 1.85/2.05
% 1.85/2.05 set(prolog_style_variables).
% 1.85/2.05 set(auto).
% 1.85/2.05 dependent: set(auto1).
% 1.85/2.05 dependent: set(process_input).
% 1.85/2.05 dependent: clear(print_kept).
% 1.85/2.05 dependent: clear(print_new_demod).
% 1.85/2.05 dependent: clear(print_back_demod).
% 1.85/2.05 dependent: clear(print_back_sub).
% 1.85/2.05 dependent: set(control_memory).
% 1.85/2.05 dependent: assign(max_mem, 12000).
% 1.85/2.05 dependent: assign(pick_given_ratio, 4).
% 1.85/2.05 dependent: assign(stats_level, 1).
% 1.85/2.05 dependent: assign(max_seconds, 10800).
% 1.85/2.05 clear(print_given).
% 1.85/2.05
% 1.85/2.05 formula_list(usable).
% 1.85/2.05 all A (A=A).
% 1.85/2.05 all W0 (aElement0(W0)->$T).
% 1.85/2.05 all W0 (aRewritingSystem0(W0)->$T).
% 1.85/2.05 all W0 W1 (aElement0(W0)&aRewritingSystem0(W1)-> (all W2 (aReductOfIn0(W2,W0,W1)->aElement0(W2)))).
% 1.85/2.05 all W0 W1 (aElement0(W0)&aElement0(W1)-> (iLess0(W0,W1)->$T)).
% 1.85/2.05 all W0 W1 W2 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)-> (sdtmndtplgtdt0(W0,W1,W2)->$T)).
% 1.85/2.05 all W0 W1 W2 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)-> (sdtmndtplgtdt0(W0,W1,W2)<->aReductOfIn0(W2,W0,W1)| (exists W3 (aElement0(W3)&aReductOfIn0(W3,W0,W1)&sdtmndtplgtdt0(W3,W1,W2))))).
% 1.85/2.05 all W0 W1 W2 W3 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)&aElement0(W3)-> (sdtmndtplgtdt0(W0,W1,W2)&sdtmndtplgtdt0(W2,W1,W3)->sdtmndtplgtdt0(W0,W1,W3))).
% 1.85/2.05 all W0 W1 W2 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)-> (sdtmndtasgtdt0(W0,W1,W2)<->W0=W2|sdtmndtplgtdt0(W0,W1,W2))).
% 1.85/2.05 all W0 W1 W2 W3 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)&aElement0(W3)-> (sdtmndtasgtdt0(W0,W1,W2)&sdtmndtasgtdt0(W2,W1,W3)->sdtmndtasgtdt0(W0,W1,W3))).
% 1.85/2.05 all W0 (aRewritingSystem0(W0)-> (isConfluent0(W0)<-> (all W1 W2 W3 (aElement0(W1)&aElement0(W2)&aElement0(W3)&sdtmndtasgtdt0(W1,W0,W2)&sdtmndtasgtdt0(W1,W0,W3)-> (exists W4 (aElement0(W4)&sdtmndtasgtdt0(W2,W0,W4)&sdtmndtasgtdt0(W3,W0,W4))))))).
% 1.85/2.05 all W0 (aRewritingSystem0(W0)-> (isLocallyConfluent0(W0)<-> (all W1 W2 W3 (aElement0(W1)&aElement0(W2)&aElement0(W3)&aReductOfIn0(W2,W1,W0)&aReductOfIn0(W3,W1,W0)-> (exists W4 (aElement0(W4)&sdtmndtasgtdt0(W2,W0,W4)&sdtmndtasgtdt0(W3,W0,W4))))))).
% 1.85/2.05 all W0 (aRewritingSystem0(W0)-> (isTerminating0(W0)<-> (all W1 W2 (aElement0(W1)&aElement0(W2)-> (sdtmndtplgtdt0(W1,W0,W2)->iLess0(W2,W1)))))).
% 1.85/2.05 all W0 W1 (aElement0(W0)&aRewritingSystem0(W1)-> (all W2 (aNormalFormOfIn0(W2,W0,W1)<->aElement0(W2)&sdtmndtasgtdt0(W0,W1,W2)& -(exists W3 aReductOfIn0(W3,W2,W1))))).
% 1.85/2.05 all W0 (aRewritingSystem0(W0)&isTerminating0(W0)-> (all W1 (aElement0(W1)-> (exists W2 aNormalFormOfIn0(W2,W1,W0))))).
% 1.85/2.05 aRewritingSystem0(xR).
% 1.85/2.05 isLocallyConfluent0(xR).
% 1.85/2.05 isTerminating0(xR).
% 1.85/2.05 all W0 W1 W2 (aElement0(W0)&aElement0(W1)&aElement0(W2)&sdtmndtasgtdt0(W0,xR,W1)&sdtmndtasgtdt0(W0,xR,W2)-> (exists W3 (aElement0(W3)&sdtmndtasgtdt0(W1,xR,W3)&sdtmndtasgtdt0(W2,xR,W3)))).
% 1.85/2.05 -isConfluent0(xR).
% 1.85/2.05 end_of_list.
% 1.85/2.05
% 1.85/2.05 -------> usable clausifies to:
% 1.85/2.05
% 1.85/2.05 list(usable).
% 1.85/2.05 0 [] A=A.
% 1.85/2.05 0 [] -aElement0(W0)|$T.
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|$T.
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aReductOfIn0(W2,W0,W1)|aElement0(W2).
% 1.85/2.05 0 [] -aElement0(W0)| -aElement0(W1)| -iLess0(W0,W1)|$T.
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|$T.
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|aReductOfIn0(W2,W0,W1)|aElement0($f1(W0,W1,W2)).
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|aReductOfIn0(W2,W0,W1)|aReductOfIn0($f1(W0,W1,W2),W0,W1).
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|aReductOfIn0(W2,W0,W1)|sdtmndtplgtdt0($f1(W0,W1,W2),W1,W2).
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtplgtdt0(W0,W1,W2)| -aReductOfIn0(W2,W0,W1).
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtplgtdt0(W0,W1,W2)| -aElement0(W3)| -aReductOfIn0(W3,W0,W1)| -sdtmndtplgtdt0(W3,W1,W2).
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtplgtdt0(W0,W1,W2)| -sdtmndtplgtdt0(W2,W1,W3)|sdtmndtplgtdt0(W0,W1,W3).
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtasgtdt0(W0,W1,W2)|W0=W2|sdtmndtplgtdt0(W0,W1,W2).
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtasgtdt0(W0,W1,W2)|W0!=W2.
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtasgtdt0(W0,W1,W2)| -sdtmndtplgtdt0(W0,W1,W2).
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtasgtdt0(W0,W1,W2)| -sdtmndtasgtdt0(W2,W1,W3)|sdtmndtasgtdt0(W0,W1,W3).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)| -isConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtasgtdt0(W1,W0,W2)| -sdtmndtasgtdt0(W1,W0,W3)|aElement0($f2(W0,W1,W2,W3)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)| -isConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtasgtdt0(W1,W0,W2)| -sdtmndtasgtdt0(W1,W0,W3)|sdtmndtasgtdt0(W2,W0,$f2(W0,W1,W2,W3)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)| -isConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtasgtdt0(W1,W0,W2)| -sdtmndtasgtdt0(W1,W0,W3)|sdtmndtasgtdt0(W3,W0,$f2(W0,W1,W2,W3)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isConfluent0(W0)|aElement0($f5(W0)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isConfluent0(W0)|aElement0($f4(W0)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isConfluent0(W0)|aElement0($f3(W0)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isConfluent0(W0)|sdtmndtasgtdt0($f5(W0),W0,$f4(W0)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isConfluent0(W0)|sdtmndtasgtdt0($f5(W0),W0,$f3(W0)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isConfluent0(W0)| -aElement0(W4)| -sdtmndtasgtdt0($f4(W0),W0,W4)| -sdtmndtasgtdt0($f3(W0),W0,W4).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)| -isLocallyConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -aReductOfIn0(W2,W1,W0)| -aReductOfIn0(W3,W1,W0)|aElement0($f6(W0,W1,W2,W3)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)| -isLocallyConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -aReductOfIn0(W2,W1,W0)| -aReductOfIn0(W3,W1,W0)|sdtmndtasgtdt0(W2,W0,$f6(W0,W1,W2,W3)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)| -isLocallyConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -aReductOfIn0(W2,W1,W0)| -aReductOfIn0(W3,W1,W0)|sdtmndtasgtdt0(W3,W0,$f6(W0,W1,W2,W3)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)|aElement0($f9(W0)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)|aElement0($f8(W0)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)|aElement0($f7(W0)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)|aReductOfIn0($f8(W0),$f9(W0),W0).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)|aReductOfIn0($f7(W0),$f9(W0),W0).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)| -aElement0(W4)| -sdtmndtasgtdt0($f8(W0),W0,W4)| -sdtmndtasgtdt0($f7(W0),W0,W4).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)| -isTerminating0(W0)| -aElement0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W1,W0,W2)|iLess0(W2,W1).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isTerminating0(W0)|aElement0($f11(W0)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isTerminating0(W0)|aElement0($f10(W0)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isTerminating0(W0)|sdtmndtplgtdt0($f11(W0),W0,$f10(W0)).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)|isTerminating0(W0)| -iLess0($f10(W0),$f11(W0)).
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aNormalFormOfIn0(W2,W0,W1)|aElement0(W2).
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aNormalFormOfIn0(W2,W0,W1)|sdtmndtasgtdt0(W0,W1,W2).
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aNormalFormOfIn0(W2,W0,W1)| -aReductOfIn0(W3,W2,W1).
% 1.85/2.05 0 [] -aElement0(W0)| -aRewritingSystem0(W1)|aNormalFormOfIn0(W2,W0,W1)| -aElement0(W2)| -sdtmndtasgtdt0(W0,W1,W2)|aReductOfIn0($f12(W0,W1,W2),W2,W1).
% 1.85/2.05 0 [] -aRewritingSystem0(W0)| -isTerminating0(W0)| -aElement0(W1)|aNormalFormOfIn0($f13(W0,W1),W1,W0).
% 1.85/2.05 0 [] aRewritingSystem0(xR).
% 1.85/2.05 0 [] isLocallyConfluent0(xR).
% 1.85/2.05 0 [] isTerminating0(xR).
% 1.85/2.05 0 [] -aElement0(W0)| -aElement0(W1)| -aElement0(W2)| -sdtmndtasgtdt0(W0,xR,W1)| -sdtmndtasgtdt0(W0,xR,W2)|aElement0($f14(W0,W1,W2)).
% 1.85/2.05 0 [] -aElement0(W0)| -aElement0(W1)| -aElement0(W2)| -sdtmndtasgtdt0(W0,xR,W1)| -sdtmndtasgtdt0(W0,xR,W2)|sdtmndtasgtdt0(W1,xR,$f14(W0,W1,W2)).
% 1.85/2.05 0 [] -aElement0(W0)| -aElement0(W1)| -aElement0(W2)| -sdtmndtasgtdt0(W0,xR,W1)| -sdtmndtasgtdt0(W0,xR,W2)|sdtmndtasgtdt0(W2,xR,$f14(W0,W1,W2)).
% 1.85/2.05 0 [] -isConfluent0(xR).
% 1.85/2.05 end_of_list.
% 1.85/2.05
% 1.85/2.05 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 1.85/2.06
% 1.85/2.06 This ia a non-Horn set with equality. The strategy will be
% 1.85/2.06 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.85/2.06 deletion, with positive clauses in sos and nonpositive
% 1.85/2.06 clauses in usable.
% 1.85/2.06
% 1.85/2.06 dependent: set(knuth_bendix).
% 1.85/2.06 dependent: set(anl_eq).
% 1.85/2.06 dependent: set(para_from).
% 1.85/2.06 dependent: set(para_into).
% 1.85/2.06 dependent: clear(para_from_right).
% 1.85/2.06 dependent: clear(para_into_right).
% 1.85/2.06 dependent: set(para_from_vars).
% 1.85/2.06 dependent: set(eq_units_both_ways).
% 1.85/2.06 dependent: set(dynamic_demod_all).
% 1.85/2.06 dependent: set(dynamic_demod).
% 1.85/2.06 dependent: set(order_eq).
% 1.85/2.06 dependent: set(back_demod).
% 1.85/2.06 dependent: set(lrpo).
% 1.85/2.06 dependent: set(hyper_res).
% 1.85/2.06 dependent: set(unit_deletion).
% 1.85/2.06 dependent: set(factor).
% 1.85/2.06
% 1.85/2.06 ------------> process usable:
% 1.85/2.06 ** KEPT (pick-wt=10): 1 [] -aElement0(A)| -aRewritingSystem0(B)| -aReductOfIn0(C,A,B)|aElement0(C).
% 1.85/2.06 ** KEPT (pick-wt=19): 2 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtplgtdt0(A,B,C)|aReductOfIn0(C,A,B)|aElement0($f1(A,B,C)).
% 1.85/2.06 ** KEPT (pick-wt=21): 3 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtplgtdt0(A,B,C)|aReductOfIn0(C,A,B)|aReductOfIn0($f1(A,B,C),A,B).
% 1.85/2.06 ** KEPT (pick-wt=21): 4 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtplgtdt0(A,B,C)|aReductOfIn0(C,A,B)|sdtmndtplgtdt0($f1(A,B,C),B,C).
% 1.85/2.06 ** KEPT (pick-wt=14): 5 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)|sdtmndtplgtdt0(A,B,C)| -aReductOfIn0(C,A,B).
% 1.85/2.06 ** KEPT (pick-wt=20): 6 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)|sdtmndtplgtdt0(A,B,C)| -aElement0(D)| -aReductOfIn0(D,A,B)| -sdtmndtplgtdt0(D,B,C).
% 1.85/2.06 ** KEPT (pick-wt=20): 7 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -aElement0(D)| -sdtmndtplgtdt0(A,B,C)| -sdtmndtplgtdt0(C,B,D)|sdtmndtplgtdt0(A,B,D).
% 1.85/2.06 ** KEPT (pick-wt=17): 8 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtasgtdt0(A,B,C)|A=C|sdtmndtplgtdt0(A,B,C).
% 1.85/2.06 ** KEPT (pick-wt=13): 9 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)|sdtmndtasgtdt0(A,B,C)|A!=C.
% 1.85/2.06 ** KEPT (pick-wt=14): 10 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)|sdtmndtasgtdt0(A,B,C)| -sdtmndtplgtdt0(A,B,C).
% 1.85/2.06 ** KEPT (pick-wt=20): 11 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -aElement0(D)| -sdtmndtasgtdt0(A,B,C)| -sdtmndtasgtdt0(C,B,D)|sdtmndtasgtdt0(A,B,D).
% 1.85/2.06 ** KEPT (pick-wt=24): 12 [] -aRewritingSystem0(A)| -isConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -sdtmndtasgtdt0(B,A,C)| -sdtmndtasgtdt0(B,A,D)|aElement0($f2(A,B,C,D)).
% 1.85/2.06 ** KEPT (pick-wt=26): 13 [] -aRewritingSystem0(A)| -isConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -sdtmndtasgtdt0(B,A,C)| -sdtmndtasgtdt0(B,A,D)|sdtmndtasgtdt0(C,A,$f2(A,B,C,D)).
% 1.85/2.06 ** KEPT (pick-wt=26): 14 [] -aRewritingSystem0(A)| -isConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -sdtmndtasgtdt0(B,A,C)| -sdtmndtasgtdt0(B,A,D)|sdtmndtasgtdt0(D,A,$f2(A,B,C,D)).
% 1.85/2.06 ** KEPT (pick-wt=7): 15 [] -aRewritingSystem0(A)|isConfluent0(A)|aElement0($f5(A)).
% 1.85/2.06 ** KEPT (pick-wt=7): 16 [] -aRewritingSystem0(A)|isConfluent0(A)|aElement0($f4(A)).
% 1.85/2.06 ** KEPT (pick-wt=7): 17 [] -aRewritingSystem0(A)|isConfluent0(A)|aElement0($f3(A)).
% 1.85/2.06 ** KEPT (pick-wt=10): 18 [] -aRewritingSystem0(A)|isConfluent0(A)|sdtmndtasgtdt0($f5(A),A,$f4(A)).
% 1.85/2.06 ** KEPT (pick-wt=10): 19 [] -aRewritingSystem0(A)|isConfluent0(A)|sdtmndtasgtdt0($f5(A),A,$f3(A)).
% 1.85/2.06 ** KEPT (pick-wt=16): 20 [] -aRewritingSystem0(A)|isConfluent0(A)| -aElement0(B)| -sdtmndtasgtdt0($f4(A),A,B)| -sdtmndtasgtdt0($f3(A),A,B).
% 1.85/2.06 ** KEPT (pick-wt=24): 21 [] -aRewritingSystem0(A)| -isLocallyConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -aReductOfIn0(C,B,A)| -aReductOfIn0(D,B,A)|aElement0($f6(A,B,C,D)).
% 1.85/2.06 ** KEPT (pick-wt=26): 22 [] -aRewritingSystem0(A)| -isLocallyConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -aReductOfIn0(C,B,A)| -aReductOfIn0(D,B,A)|sdtmndtasgtdt0(C,A,$f6(A,B,C,D)).
% 1.85/2.06 ** KEPT (pick-wt=26): 23 [] -aRewritingSystem0(A)| -isLocallyConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -aReductOfIn0(C,B,A)| -aReductOfIn0(D,B,A)|sdtmndtasgtdt0(D,A,$f6(A,B,C,D)).
% 1.85/2.06 ** KEPT (pick-wt=7): 24 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)|aElement0($f9(A)).
% 3.49/3.68 ** KEPT (pick-wt=7): 25 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)|aElement0($f8(A)).
% 3.49/3.68 ** KEPT (pick-wt=7): 26 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)|aElement0($f7(A)).
% 3.49/3.68 ** KEPT (pick-wt=10): 27 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)|aReductOfIn0($f8(A),$f9(A),A).
% 3.49/3.68 ** KEPT (pick-wt=10): 28 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)|aReductOfIn0($f7(A),$f9(A),A).
% 3.49/3.68 ** KEPT (pick-wt=16): 29 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)| -aElement0(B)| -sdtmndtasgtdt0($f8(A),A,B)| -sdtmndtasgtdt0($f7(A),A,B).
% 3.49/3.68 ** KEPT (pick-wt=15): 30 [] -aRewritingSystem0(A)| -isTerminating0(A)| -aElement0(B)| -aElement0(C)| -sdtmndtplgtdt0(B,A,C)|iLess0(C,B).
% 3.49/3.68 ** KEPT (pick-wt=7): 31 [] -aRewritingSystem0(A)|isTerminating0(A)|aElement0($f11(A)).
% 3.49/3.68 ** KEPT (pick-wt=7): 32 [] -aRewritingSystem0(A)|isTerminating0(A)|aElement0($f10(A)).
% 3.49/3.68 ** KEPT (pick-wt=10): 33 [] -aRewritingSystem0(A)|isTerminating0(A)|sdtmndtplgtdt0($f11(A),A,$f10(A)).
% 3.49/3.68 ** KEPT (pick-wt=9): 34 [] -aRewritingSystem0(A)|isTerminating0(A)| -iLess0($f10(A),$f11(A)).
% 3.49/3.68 ** KEPT (pick-wt=10): 35 [] -aElement0(A)| -aRewritingSystem0(B)| -aNormalFormOfIn0(C,A,B)|aElement0(C).
% 3.49/3.68 ** KEPT (pick-wt=12): 36 [] -aElement0(A)| -aRewritingSystem0(B)| -aNormalFormOfIn0(C,A,B)|sdtmndtasgtdt0(A,B,C).
% 3.49/3.68 ** KEPT (pick-wt=12): 37 [] -aElement0(A)| -aRewritingSystem0(B)| -aNormalFormOfIn0(C,A,B)| -aReductOfIn0(D,C,B).
% 3.49/3.68 ** KEPT (pick-wt=21): 38 [] -aElement0(A)| -aRewritingSystem0(B)|aNormalFormOfIn0(C,A,B)| -aElement0(C)| -sdtmndtasgtdt0(A,B,C)|aReductOfIn0($f12(A,B,C),C,B).
% 3.49/3.68 ** KEPT (pick-wt=12): 39 [] -aRewritingSystem0(A)| -isTerminating0(A)| -aElement0(B)|aNormalFormOfIn0($f13(A,B),B,A).
% 3.49/3.68 ** KEPT (pick-wt=19): 40 [] -aElement0(A)| -aElement0(B)| -aElement0(C)| -sdtmndtasgtdt0(A,xR,B)| -sdtmndtasgtdt0(A,xR,C)|aElement0($f14(A,B,C)).
% 3.49/3.68 ** KEPT (pick-wt=21): 41 [] -aElement0(A)| -aElement0(B)| -aElement0(C)| -sdtmndtasgtdt0(A,xR,B)| -sdtmndtasgtdt0(A,xR,C)|sdtmndtasgtdt0(B,xR,$f14(A,B,C)).
% 3.49/3.68 ** KEPT (pick-wt=21): 42 [] -aElement0(A)| -aElement0(B)| -aElement0(C)| -sdtmndtasgtdt0(A,xR,B)| -sdtmndtasgtdt0(A,xR,C)|sdtmndtasgtdt0(C,xR,$f14(A,B,C)).
% 3.49/3.68 ** KEPT (pick-wt=2): 43 [] -isConfluent0(xR).
% 3.49/3.68
% 3.49/3.68 ------------> process sos:
% 3.49/3.68 ** KEPT (pick-wt=3): 86 [] A=A.
% 3.49/3.68 ** KEPT (pick-wt=2): 87 [] aRewritingSystem0(xR).
% 3.49/3.68 ** KEPT (pick-wt=2): 88 [] isLocallyConfluent0(xR).
% 3.49/3.68 ** KEPT (pick-wt=2): 89 [] isTerminating0(xR).
% 3.49/3.68 Following clause subsumed by 86 during input processing: 0 [copy,86,flip.1] A=A.
% 3.49/3.68 86 back subsumes 50.
% 3.49/3.68
% 3.49/3.68 ======= end of input processing =======
% 3.49/3.68
% 3.49/3.68 =========== start of search ===========
% 3.49/3.68
% 3.49/3.68 -------- PROOF --------
% 3.49/3.68
% 3.49/3.68 ----> UNIT CONFLICT at 1.64 sec ----> 1023 [binary,1022.1,43.1] $F.
% 3.49/3.68
% 3.49/3.68 Length of proof is 9. Level of proof is 3.
% 3.49/3.68
% 3.49/3.68 ---------------- PROOF ----------------
% 3.49/3.68 % SZS status Theorem
% 3.49/3.68 % SZS output start Refutation
% See solution above
% 3.49/3.69 ------------ end of proof -------------
% 3.49/3.69
% 3.49/3.69
% 3.49/3.69 Search stopped by max_proofs option.
% 3.49/3.69
% 3.49/3.69
% 3.49/3.69 Search stopped by max_proofs option.
% 3.49/3.69
% 3.49/3.69 ============ end of search ============
% 3.49/3.69
% 3.49/3.69 -------------- statistics -------------
% 3.49/3.69 clauses given 77
% 3.49/3.69 clauses generated 2094
% 3.49/3.69 clauses kept 1022
% 3.49/3.69 clauses forward subsumed 1066
% 3.49/3.69 clauses back subsumed 3
% 3.49/3.69 Kbytes malloced 2929
% 3.49/3.69
% 3.49/3.69 ----------- times (seconds) -----------
% 3.49/3.69 user CPU time 1.64 (0 hr, 0 min, 1 sec)
% 3.49/3.69 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.49/3.69 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.49/3.69
% 3.49/3.69 That finishes the proof of the theorem.
% 3.49/3.69
% 3.49/3.69 Process 4469 finished Wed Jul 27 06:45:17 2022
% 3.49/3.69 Otter interrupted
% 3.49/3.69 PROOF FOUND
%------------------------------------------------------------------------------