TSTP Solution File: COM013+4 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COM013+4 : 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 12:48:22 EDT 2022
% Result : Theorem 2.41s 2.66s
% Output : Refutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of clauses : 23 ( 13 unt; 0 nHn; 22 RR)
% Number of literals : 53 ( 2 equ; 31 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 22 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ aElement0(A)
| ~ aRewritingSystem0(B)
| ~ aReductOfIn0(C,A,B)
| aElement0(C) ),
file('COM013+4.p',unknown),
[] ).
cnf(5,axiom,
( ~ aElement0(A)
| ~ aRewritingSystem0(B)
| ~ aElement0(C)
| sdtmndtplgtdt0(A,B,C)
| ~ aReductOfIn0(C,A,B) ),
file('COM013+4.p',unknown),
[] ).
cnf(10,axiom,
( ~ aElement0(A)
| ~ aRewritingSystem0(B)
| ~ aElement0(C)
| sdtmndtasgtdt0(A,B,C)
| ~ sdtmndtplgtdt0(A,B,C) ),
file('COM013+4.p',unknown),
[] ).
cnf(11,axiom,
( ~ aElement0(A)
| ~ aRewritingSystem0(B)
| ~ aElement0(C)
| ~ aElement0(D)
| ~ sdtmndtasgtdt0(A,B,C)
| ~ sdtmndtasgtdt0(C,B,D)
| sdtmndtasgtdt0(A,B,D) ),
file('COM013+4.p',unknown),
[] ).
cnf(39,axiom,
( ~ aElement0(A)
| ~ aElement0(B)
| ~ aReductOfIn0(B,A,xR)
| iLess0(B,A) ),
file('COM013+4.p',unknown),
[] ).
cnf(42,axiom,
( ~ aElement0(A)
| ~ iLess0(A,dollar_c1)
| aElement0(dollar_f14(A)) ),
file('COM013+4.p',unknown),
[] ).
cnf(51,axiom,
( ~ aElement0(A)
| ~ iLess0(A,dollar_c1)
| sdtmndtasgtdt0(A,xR,dollar_f14(A)) ),
file('COM013+4.p',unknown),
[] ).
cnf(52,axiom,
( ~ aElement0(A)
| ~ iLess0(A,dollar_c1)
| ~ aReductOfIn0(B,dollar_f14(A),xR) ),
file('COM013+4.p',unknown),
[] ).
cnf(54,axiom,
( ~ aElement0(A)
| dollar_c1 != A
| aReductOfIn0(dollar_f15(A),A,xR) ),
file('COM013+4.p',unknown),
[] ).
cnf(58,axiom,
( ~ aElement0(A)
| ~ sdtmndtasgtdt0(dollar_c1,xR,A)
| aReductOfIn0(dollar_f15(A),A,xR) ),
file('COM013+4.p',unknown),
[] ).
cnf(95,axiom,
A = A,
file('COM013+4.p',unknown),
[] ).
cnf(96,axiom,
aRewritingSystem0(xR),
file('COM013+4.p',unknown),
[] ).
cnf(98,axiom,
aElement0(dollar_c1),
file('COM013+4.p',unknown),
[] ).
cnf(112,plain,
aReductOfIn0(dollar_f15(dollar_c1),dollar_c1,xR),
inference(hyper,[status(thm)],[98,54,95]),
[iquote('hyper,98,54,95')] ).
cnf(147,plain,
aElement0(dollar_f15(dollar_c1)),
inference(hyper,[status(thm)],[112,1,98,96]),
[iquote('hyper,112,1,98,96')] ).
cnf(164,plain,
iLess0(dollar_f15(dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[147,39,98,112]),
[iquote('hyper,147,39,98,112')] ).
cnf(165,plain,
sdtmndtplgtdt0(dollar_c1,xR,dollar_f15(dollar_c1)),
inference(hyper,[status(thm)],[147,5,98,96,112]),
[iquote('hyper,147,5,98,96,112')] ).
cnf(176,plain,
sdtmndtasgtdt0(dollar_f15(dollar_c1),xR,dollar_f14(dollar_f15(dollar_c1))),
inference(hyper,[status(thm)],[164,51,147]),
[iquote('hyper,164,51,147')] ).
cnf(181,plain,
aElement0(dollar_f14(dollar_f15(dollar_c1))),
inference(hyper,[status(thm)],[164,42,147]),
[iquote('hyper,164,42,147')] ).
cnf(188,plain,
sdtmndtasgtdt0(dollar_c1,xR,dollar_f15(dollar_c1)),
inference(hyper,[status(thm)],[165,10,98,96,147]),
[iquote('hyper,165,10,98,96,147')] ).
cnf(418,plain,
sdtmndtasgtdt0(dollar_c1,xR,dollar_f14(dollar_f15(dollar_c1))),
inference(hyper,[status(thm)],[176,11,98,96,147,181,188]),
[iquote('hyper,176,11,98,96,147,181,188')] ).
cnf(465,plain,
aReductOfIn0(dollar_f15(dollar_f14(dollar_f15(dollar_c1))),dollar_f14(dollar_f15(dollar_c1)),xR),
inference(hyper,[status(thm)],[418,58,181]),
[iquote('hyper,418,58,181')] ).
cnf(1049,plain,
$false,
inference(hyper,[status(thm)],[465,52,147,164]),
[iquote('hyper,465,52,147,164')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM013+4 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 06:34:35 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.92/2.15 ----- Otter 3.3f, August 2004 -----
% 1.92/2.15 The process was started by sandbox on n022.cluster.edu,
% 1.92/2.15 Wed Jul 27 06:34:35 2022
% 1.92/2.15 The command was "./otter". The process ID is 5305.
% 1.92/2.15
% 1.92/2.15 set(prolog_style_variables).
% 1.92/2.15 set(auto).
% 1.92/2.15 dependent: set(auto1).
% 1.92/2.15 dependent: set(process_input).
% 1.92/2.15 dependent: clear(print_kept).
% 1.92/2.15 dependent: clear(print_new_demod).
% 1.92/2.15 dependent: clear(print_back_demod).
% 1.92/2.15 dependent: clear(print_back_sub).
% 1.92/2.15 dependent: set(control_memory).
% 1.92/2.15 dependent: assign(max_mem, 12000).
% 1.92/2.15 dependent: assign(pick_given_ratio, 4).
% 1.92/2.15 dependent: assign(stats_level, 1).
% 1.92/2.15 dependent: assign(max_seconds, 10800).
% 1.92/2.15 clear(print_given).
% 1.92/2.15
% 1.92/2.15 formula_list(usable).
% 1.92/2.15 all A (A=A).
% 1.92/2.15 all W0 (aElement0(W0)->$T).
% 1.92/2.15 all W0 (aRewritingSystem0(W0)->$T).
% 1.92/2.15 all W0 W1 (aElement0(W0)&aRewritingSystem0(W1)-> (all W2 (aReductOfIn0(W2,W0,W1)->aElement0(W2)))).
% 1.92/2.15 all W0 W1 (aElement0(W0)&aElement0(W1)-> (iLess0(W0,W1)->$T)).
% 1.92/2.15 all W0 W1 W2 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)-> (sdtmndtplgtdt0(W0,W1,W2)->$T)).
% 1.92/2.15 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))))).
% 1.92/2.15 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))).
% 1.92/2.15 all W0 W1 W2 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)-> (sdtmndtasgtdt0(W0,W1,W2)<->W0=W2|sdtmndtplgtdt0(W0,W1,W2))).
% 1.92/2.15 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))).
% 1.92/2.15 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))))))).
% 1.92/2.15 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))))))).
% 1.92/2.15 all W0 (aRewritingSystem0(W0)-> (isTerminating0(W0)<-> (all W1 W2 (aElement0(W1)&aElement0(W2)-> (sdtmndtplgtdt0(W1,W0,W2)->iLess0(W2,W1)))))).
% 1.92/2.15 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))))).
% 1.92/2.15 aRewritingSystem0(xR).
% 1.92/2.15 all W0 W1 (aElement0(W0)&aElement0(W1)-> (aReductOfIn0(W1,W0,xR)| (exists W2 (aElement0(W2)&aReductOfIn0(W2,W0,xR)&sdtmndtplgtdt0(W2,xR,W1)))|sdtmndtplgtdt0(W0,xR,W1)->iLess0(W1,W0))).
% 1.92/2.15 isTerminating0(xR).
% 1.92/2.15 -(all W0 (aElement0(W0)-> ((all W1 (aElement0(W1)-> (iLess0(W1,W0)-> (exists W2 (aElement0(W2)& (W1=W2| (aReductOfIn0(W2,W1,xR)| (exists W3 (aElement0(W3)&aReductOfIn0(W3,W1,xR)&sdtmndtplgtdt0(W3,xR,W2))))&sdtmndtplgtdt0(W1,xR,W2))&sdtmndtasgtdt0(W1,xR,W2)& -(exists W3 aReductOfIn0(W3,W2,xR))&aNormalFormOfIn0(W2,W1,xR))))))-> (exists W1 (aElement0(W1)& (W0=W1|aReductOfIn0(W1,W0,xR)| (exists W2 (aElement0(W2)&aReductOfIn0(W2,W0,xR)&sdtmndtplgtdt0(W2,xR,W1)))|sdtmndtplgtdt0(W0,xR,W1)|sdtmndtasgtdt0(W0,xR,W1))& -(exists W2 aReductOfIn0(W2,W1,xR))|aNormalFormOfIn0(W1,W0,xR)))))).
% 1.92/2.15 end_of_list.
% 1.92/2.15
% 1.92/2.15 -------> usable clausifies to:
% 1.92/2.15
% 1.92/2.15 list(usable).
% 1.92/2.15 0 [] A=A.
% 1.92/2.15 0 [] -aElement0(W0)|$T.
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|$T.
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aReductOfIn0(W2,W0,W1)|aElement0(W2).
% 1.92/2.15 0 [] -aElement0(W0)| -aElement0(W1)| -iLess0(W0,W1)|$T.
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|$T.
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|aReductOfIn0(W2,W0,W1)|aElement0($f1(W0,W1,W2)).
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|aReductOfIn0(W2,W0,W1)|aReductOfIn0($f1(W0,W1,W2),W0,W1).
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|aReductOfIn0(W2,W0,W1)|sdtmndtplgtdt0($f1(W0,W1,W2),W1,W2).
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtplgtdt0(W0,W1,W2)| -aReductOfIn0(W2,W0,W1).
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtplgtdt0(W0,W1,W2)| -aElement0(W3)| -aReductOfIn0(W3,W0,W1)| -sdtmndtplgtdt0(W3,W1,W2).
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtplgtdt0(W0,W1,W2)| -sdtmndtplgtdt0(W2,W1,W3)|sdtmndtplgtdt0(W0,W1,W3).
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtasgtdt0(W0,W1,W2)|W0=W2|sdtmndtplgtdt0(W0,W1,W2).
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtasgtdt0(W0,W1,W2)|W0!=W2.
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtasgtdt0(W0,W1,W2)| -sdtmndtplgtdt0(W0,W1,W2).
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtasgtdt0(W0,W1,W2)| -sdtmndtasgtdt0(W2,W1,W3)|sdtmndtasgtdt0(W0,W1,W3).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)| -isConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtasgtdt0(W1,W0,W2)| -sdtmndtasgtdt0(W1,W0,W3)|aElement0($f2(W0,W1,W2,W3)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)| -isConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtasgtdt0(W1,W0,W2)| -sdtmndtasgtdt0(W1,W0,W3)|sdtmndtasgtdt0(W2,W0,$f2(W0,W1,W2,W3)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)| -isConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtasgtdt0(W1,W0,W2)| -sdtmndtasgtdt0(W1,W0,W3)|sdtmndtasgtdt0(W3,W0,$f2(W0,W1,W2,W3)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isConfluent0(W0)|aElement0($f5(W0)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isConfluent0(W0)|aElement0($f4(W0)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isConfluent0(W0)|aElement0($f3(W0)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isConfluent0(W0)|sdtmndtasgtdt0($f5(W0),W0,$f4(W0)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isConfluent0(W0)|sdtmndtasgtdt0($f5(W0),W0,$f3(W0)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isConfluent0(W0)| -aElement0(W4)| -sdtmndtasgtdt0($f4(W0),W0,W4)| -sdtmndtasgtdt0($f3(W0),W0,W4).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)| -isLocallyConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -aReductOfIn0(W2,W1,W0)| -aReductOfIn0(W3,W1,W0)|aElement0($f6(W0,W1,W2,W3)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)| -isLocallyConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -aReductOfIn0(W2,W1,W0)| -aReductOfIn0(W3,W1,W0)|sdtmndtasgtdt0(W2,W0,$f6(W0,W1,W2,W3)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)| -isLocallyConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -aReductOfIn0(W2,W1,W0)| -aReductOfIn0(W3,W1,W0)|sdtmndtasgtdt0(W3,W0,$f6(W0,W1,W2,W3)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)|aElement0($f9(W0)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)|aElement0($f8(W0)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)|aElement0($f7(W0)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)|aReductOfIn0($f8(W0),$f9(W0),W0).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)|aReductOfIn0($f7(W0),$f9(W0),W0).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)| -aElement0(W4)| -sdtmndtasgtdt0($f8(W0),W0,W4)| -sdtmndtasgtdt0($f7(W0),W0,W4).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)| -isTerminating0(W0)| -aElement0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W1,W0,W2)|iLess0(W2,W1).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isTerminating0(W0)|aElement0($f11(W0)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isTerminating0(W0)|aElement0($f10(W0)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isTerminating0(W0)|sdtmndtplgtdt0($f11(W0),W0,$f10(W0)).
% 1.92/2.15 0 [] -aRewritingSystem0(W0)|isTerminating0(W0)| -iLess0($f10(W0),$f11(W0)).
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aNormalFormOfIn0(W2,W0,W1)|aElement0(W2).
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aNormalFormOfIn0(W2,W0,W1)|sdtmndtasgtdt0(W0,W1,W2).
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aNormalFormOfIn0(W2,W0,W1)| -aReductOfIn0(W3,W2,W1).
% 1.92/2.15 0 [] -aElement0(W0)| -aRewritingSystem0(W1)|aNormalFormOfIn0(W2,W0,W1)| -aElement0(W2)| -sdtmndtasgtdt0(W0,W1,W2)|aReductOfIn0($f12(W0,W1,W2),W2,W1).
% 1.92/2.15 0 [] aRewritingSystem0(xR).
% 1.92/2.15 0 [] -aElement0(W0)| -aElement0(W1)| -aReductOfIn0(W1,W0,xR)|iLess0(W1,W0).
% 1.92/2.15 0 [] -aElement0(W0)| -aElement0(W1)| -aElement0(W2)| -aReductOfIn0(W2,W0,xR)| -sdtmndtplgtdt0(W2,xR,W1)|iLess0(W1,W0).
% 1.92/2.15 0 [] -aElement0(W0)| -aElement0(W1)| -sdtmndtplgtdt0(W0,xR,W1)|iLess0(W1,W0).
% 1.92/2.16 0 [] isTerminating0(xR).
% 1.92/2.16 0 [] aElement0($c1).
% 1.92/2.16 0 [] -aElement0(W1)| -iLess0(W1,$c1)|aElement0($f14(W1)).
% 1.92/2.16 0 [] -aElement0(W1)| -iLess0(W1,$c1)|W1=$f14(W1)|aReductOfIn0($f14(W1),W1,xR)|aElement0($f13(W1)).
% 1.92/2.16 0 [] -aElement0(W1)| -iLess0(W1,$c1)|W1=$f14(W1)|aReductOfIn0($f14(W1),W1,xR)|aReductOfIn0($f13(W1),W1,xR).
% 1.92/2.16 0 [] -aElement0(W1)| -iLess0(W1,$c1)|W1=$f14(W1)|aReductOfIn0($f14(W1),W1,xR)|sdtmndtplgtdt0($f13(W1),xR,$f14(W1)).
% 1.92/2.16 0 [] -aElement0(W1)| -iLess0(W1,$c1)|W1=$f14(W1)|sdtmndtplgtdt0(W1,xR,$f14(W1)).
% 1.92/2.16 0 [] -aElement0(W1)| -iLess0(W1,$c1)|sdtmndtasgtdt0(W1,xR,$f14(W1)).
% 1.92/2.16 0 [] -aElement0(W1)| -iLess0(W1,$c1)| -aReductOfIn0(W3,$f14(W1),xR).
% 1.92/2.16 0 [] -aElement0(W1)| -iLess0(W1,$c1)|aNormalFormOfIn0($f14(W1),W1,xR).
% 1.92/2.16 0 [] -aElement0(X1)|$c1!=X1|aReductOfIn0($f15(X1),X1,xR).
% 1.92/2.16 0 [] -aElement0(X1)| -aReductOfIn0(X1,$c1,xR)|aReductOfIn0($f15(X1),X1,xR).
% 1.92/2.16 0 [] -aElement0(X1)| -aElement0(W2)| -aReductOfIn0(W2,$c1,xR)| -sdtmndtplgtdt0(W2,xR,X1)|aReductOfIn0($f15(X1),X1,xR).
% 1.92/2.16 0 [] -aElement0(X1)| -sdtmndtplgtdt0($c1,xR,X1)|aReductOfIn0($f15(X1),X1,xR).
% 1.92/2.16 0 [] -aElement0(X1)| -sdtmndtasgtdt0($c1,xR,X1)|aReductOfIn0($f15(X1),X1,xR).
% 1.92/2.16 0 [] -aNormalFormOfIn0(X1,$c1,xR).
% 1.92/2.16 end_of_list.
% 1.92/2.16
% 1.92/2.16 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 1.92/2.16
% 1.92/2.16 This ia a non-Horn set with equality. The strategy will be
% 1.92/2.16 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.92/2.16 deletion, with positive clauses in sos and nonpositive
% 1.92/2.16 clauses in usable.
% 1.92/2.16
% 1.92/2.16 dependent: set(knuth_bendix).
% 1.92/2.16 dependent: set(anl_eq).
% 1.92/2.16 dependent: set(para_from).
% 1.92/2.16 dependent: set(para_into).
% 1.92/2.16 dependent: clear(para_from_right).
% 1.92/2.16 dependent: clear(para_into_right).
% 1.92/2.16 dependent: set(para_from_vars).
% 1.92/2.16 dependent: set(eq_units_both_ways).
% 1.92/2.16 dependent: set(dynamic_demod_all).
% 1.92/2.16 dependent: set(dynamic_demod).
% 1.92/2.16 dependent: set(order_eq).
% 1.92/2.16 dependent: set(back_demod).
% 1.92/2.16 dependent: set(lrpo).
% 1.92/2.16 dependent: set(hyper_res).
% 1.92/2.16 dependent: set(unit_deletion).
% 1.92/2.16 dependent: set(factor).
% 1.92/2.16
% 1.92/2.16 ------------> process usable:
% 1.92/2.16 ** KEPT (pick-wt=10): 1 [] -aElement0(A)| -aRewritingSystem0(B)| -aReductOfIn0(C,A,B)|aElement0(C).
% 1.92/2.16 ** KEPT (pick-wt=19): 2 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtplgtdt0(A,B,C)|aReductOfIn0(C,A,B)|aElement0($f1(A,B,C)).
% 1.92/2.16 ** KEPT (pick-wt=21): 3 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtplgtdt0(A,B,C)|aReductOfIn0(C,A,B)|aReductOfIn0($f1(A,B,C),A,B).
% 1.92/2.16 ** KEPT (pick-wt=21): 4 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtplgtdt0(A,B,C)|aReductOfIn0(C,A,B)|sdtmndtplgtdt0($f1(A,B,C),B,C).
% 1.92/2.16 ** KEPT (pick-wt=14): 5 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)|sdtmndtplgtdt0(A,B,C)| -aReductOfIn0(C,A,B).
% 1.92/2.16 ** 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).
% 1.92/2.16 ** 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).
% 1.92/2.16 ** KEPT (pick-wt=17): 8 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtasgtdt0(A,B,C)|A=C|sdtmndtplgtdt0(A,B,C).
% 1.92/2.16 ** KEPT (pick-wt=13): 9 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)|sdtmndtasgtdt0(A,B,C)|A!=C.
% 1.92/2.16 ** KEPT (pick-wt=14): 10 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)|sdtmndtasgtdt0(A,B,C)| -sdtmndtplgtdt0(A,B,C).
% 1.92/2.16 ** 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).
% 1.92/2.16 ** KEPT (pick-wt=24): 12 [] -aRewritingSystem0(A)| -isConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -sdtmndtasgtdt0(B,A,C)| -sdtmndtasgtdt0(B,A,D)|aElement0($f2(A,B,C,D)).
% 1.92/2.16 ** KEPT (pick-wt=26): 13 [] -aRewritingSystem0(A)| -isConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -sdtmndtasgtdt0(B,A,C)| -sdtmndtasgtdt0(B,A,D)|sdtmndtasgtdt0(C,A,$f2(A,B,C,D)).
% 1.92/2.16 ** 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,$f2(A,B,C,D)).
% 1.92/2.16 ** KEPT (pick-wt=7): 15 [] -aRewritingSystem0(A)|isConfluent0(A)|aElement0($f5(A)).
% 1.92/2.16 ** KEPT (pick-wt=7): 16 [] -aRewritingSystem0(A)|isConfluent0(A)|aElement0($f4(A)).
% 1.92/2.16 ** KEPT (pick-wt=7): 17 [] -aRewritingSystem0(A)|isConfluent0(A)|aElement0($f3(A)).
% 1.92/2.16 ** KEPT (pick-wt=10): 18 [] -aRewritingSystem0(A)|isConfluent0(A)|sdtmndtasgtdt0($f5(A),A,$f4(A)).
% 1.92/2.16 ** KEPT (pick-wt=10): 19 [] -aRewritingSystem0(A)|isConfluent0(A)|sdtmndtasgtdt0($f5(A),A,$f3(A)).
% 1.92/2.16 ** KEPT (pick-wt=16): 20 [] -aRewritingSystem0(A)|isConfluent0(A)| -aElement0(B)| -sdtmndtasgtdt0($f4(A),A,B)| -sdtmndtasgtdt0($f3(A),A,B).
% 1.92/2.16 ** KEPT (pick-wt=24): 21 [] -aRewritingSystem0(A)| -isLocallyConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -aReductOfIn0(C,B,A)| -aReductOfIn0(D,B,A)|aElement0($f6(A,B,C,D)).
% 1.92/2.16 ** KEPT (pick-wt=26): 22 [] -aRewritingSystem0(A)| -isLocallyConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -aReductOfIn0(C,B,A)| -aReductOfIn0(D,B,A)|sdtmndtasgtdt0(C,A,$f6(A,B,C,D)).
% 1.92/2.16 ** 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,$f6(A,B,C,D)).
% 1.92/2.16 ** KEPT (pick-wt=7): 24 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)|aElement0($f9(A)).
% 1.92/2.16 ** KEPT (pick-wt=7): 25 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)|aElement0($f8(A)).
% 1.92/2.16 ** KEPT (pick-wt=7): 26 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)|aElement0($f7(A)).
% 1.92/2.16 ** KEPT (pick-wt=10): 27 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)|aReductOfIn0($f8(A),$f9(A),A).
% 1.92/2.16 ** KEPT (pick-wt=10): 28 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)|aReductOfIn0($f7(A),$f9(A),A).
% 1.92/2.16 ** KEPT (pick-wt=16): 29 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)| -aElement0(B)| -sdtmndtasgtdt0($f8(A),A,B)| -sdtmndtasgtdt0($f7(A),A,B).
% 1.92/2.16 ** KEPT (pick-wt=15): 30 [] -aRewritingSystem0(A)| -isTerminating0(A)| -aElement0(B)| -aElement0(C)| -sdtmndtplgtdt0(B,A,C)|iLess0(C,B).
% 1.92/2.16 ** KEPT (pick-wt=7): 31 [] -aRewritingSystem0(A)|isTerminating0(A)|aElement0($f11(A)).
% 1.92/2.16 ** KEPT (pick-wt=7): 32 [] -aRewritingSystem0(A)|isTerminating0(A)|aElement0($f10(A)).
% 1.92/2.16 ** KEPT (pick-wt=10): 33 [] -aRewritingSystem0(A)|isTerminating0(A)|sdtmndtplgtdt0($f11(A),A,$f10(A)).
% 1.92/2.16 ** KEPT (pick-wt=9): 34 [] -aRewritingSystem0(A)|isTerminating0(A)| -iLess0($f10(A),$f11(A)).
% 1.92/2.16 ** KEPT (pick-wt=10): 35 [] -aElement0(A)| -aRewritingSystem0(B)| -aNormalFormOfIn0(C,A,B)|aElement0(C).
% 1.92/2.16 ** KEPT (pick-wt=12): 36 [] -aElement0(A)| -aRewritingSystem0(B)| -aNormalFormOfIn0(C,A,B)|sdtmndtasgtdt0(A,B,C).
% 1.92/2.16 ** KEPT (pick-wt=12): 37 [] -aElement0(A)| -aRewritingSystem0(B)| -aNormalFormOfIn0(C,A,B)| -aReductOfIn0(D,C,B).
% 1.92/2.16 ** KEPT (pick-wt=21): 38 [] -aElement0(A)| -aRewritingSystem0(B)|aNormalFormOfIn0(C,A,B)| -aElement0(C)| -sdtmndtasgtdt0(A,B,C)|aReductOfIn0($f12(A,B,C),C,B).
% 1.92/2.16 ** KEPT (pick-wt=11): 39 [] -aElement0(A)| -aElement0(B)| -aReductOfIn0(B,A,xR)|iLess0(B,A).
% 1.92/2.16 ** KEPT (pick-wt=17): 40 [] -aElement0(A)| -aElement0(B)| -aElement0(C)| -aReductOfIn0(C,A,xR)| -sdtmndtplgtdt0(C,xR,B)|iLess0(B,A).
% 1.92/2.16 ** KEPT (pick-wt=11): 41 [] -aElement0(A)| -aElement0(B)| -sdtmndtplgtdt0(A,xR,B)|iLess0(B,A).
% 1.92/2.16 ** KEPT (pick-wt=8): 42 [] -aElement0(A)| -iLess0(A,$c1)|aElement0($f14(A)).
% 1.92/2.16 ** KEPT (pick-wt=17): 44 [copy,43,flip.3] -aElement0(A)| -iLess0(A,$c1)|$f14(A)=A|aReductOfIn0($f14(A),A,xR)|aElement0($f13(A)).
% 1.92/2.16 ** KEPT (pick-wt=19): 46 [copy,45,flip.3] -aElement0(A)| -iLess0(A,$c1)|$f14(A)=A|aReductOfIn0($f14(A),A,xR)|aReductOfIn0($f13(A),A,xR).
% 1.92/2.16 ** KEPT (pick-wt=20): 48 [copy,47,flip.3] -aElement0(A)| -iLess0(A,$c1)|$f14(A)=A|aReductOfIn0($f14(A),A,xR)|sdtmndtplgtdt0($f13(A),xR,$f14(A)).
% 1.92/2.16 ** KEPT (pick-wt=14): 50 [copy,49,flip.3] -aElement0(A)| -iLess0(A,$c1)|$f14(A)=A|sdtmndtplgtdt0(A,xR,$f14(A)).
% 1.92/2.16 ** KEPT (pick-wt=10): 51 [] -aElement0(A)| -iLess0(A,$c1)|sdtmndtasgtdt0(A,xR,$f14(A)).
% 1.92/2.16 ** KEPT (pick-wt=10): 52 [] -aElement0(A)| -iLess0(A,$c1)| -aReductOfIn0(B,$f14(A),xR).
% 1.92/2.16 ** KEPT (pick-wt=10): 53 [] -aElement0(A)| -iLess0(A,$c1)|aNormalFormOfIn0($f14(A),A,xR).
% 1.92/2.16 ** KEPT (pick-wt=10): 54 [] -aElement0(A)|$c1!=A|aReductOfIn0($f15(A),A,xR).
% 2.41/2.66 ** KEPT (pick-wt=11): 55 [] -aElement0(A)| -aReductOfIn0(A,$c1,xR)|aReductOfIn0($f15(A),A,xR).
% 2.41/2.66 ** KEPT (pick-wt=17): 56 [] -aElement0(A)| -aElement0(B)| -aReductOfIn0(B,$c1,xR)| -sdtmndtplgtdt0(B,xR,A)|aReductOfIn0($f15(A),A,xR).
% 2.41/2.66 ** KEPT (pick-wt=11): 57 [] -aElement0(A)| -sdtmndtplgtdt0($c1,xR,A)|aReductOfIn0($f15(A),A,xR).
% 2.41/2.66 ** KEPT (pick-wt=11): 58 [] -aElement0(A)| -sdtmndtasgtdt0($c1,xR,A)|aReductOfIn0($f15(A),A,xR).
% 2.41/2.66 ** KEPT (pick-wt=4): 59 [] -aNormalFormOfIn0(A,$c1,xR).
% 2.41/2.66
% 2.41/2.66 ------------> process sos:
% 2.41/2.66 ** KEPT (pick-wt=3): 95 [] A=A.
% 2.41/2.66 ** KEPT (pick-wt=2): 96 [] aRewritingSystem0(xR).
% 2.41/2.66 ** KEPT (pick-wt=2): 97 [] isTerminating0(xR).
% 2.41/2.66 ** KEPT (pick-wt=2): 98 [] aElement0($c1).
% 2.41/2.66 Following clause subsumed by 95 during input processing: 0 [copy,95,flip.1] A=A.
% 2.41/2.66 95 back subsumes 66.
% 2.41/2.66
% 2.41/2.66 ======= end of input processing =======
% 2.41/2.66
% 2.41/2.66 =========== start of search ===========
% 2.41/2.66
% 2.41/2.66 -------- PROOF --------
% 2.41/2.66
% 2.41/2.66 -----> EMPTY CLAUSE at 0.51 sec ----> 1049 [hyper,465,52,147,164] $F.
% 2.41/2.66
% 2.41/2.66 Length of proof is 9. Level of proof is 6.
% 2.41/2.66
% 2.41/2.66 ---------------- PROOF ----------------
% 2.41/2.66 % SZS status Theorem
% 2.41/2.66 % SZS output start Refutation
% See solution above
% 2.41/2.66 ------------ end of proof -------------
% 2.41/2.66
% 2.41/2.66
% 2.41/2.66 Search stopped by max_proofs option.
% 2.41/2.66
% 2.41/2.66
% 2.41/2.66 Search stopped by max_proofs option.
% 2.41/2.66
% 2.41/2.66 ============ end of search ============
% 2.41/2.66
% 2.41/2.66 -------------- statistics -------------
% 2.41/2.66 clauses given 55
% 2.41/2.66 clauses generated 2296
% 2.41/2.66 clauses kept 1044
% 2.41/2.66 clauses forward subsumed 1279
% 2.41/2.66 clauses back subsumed 1
% 2.41/2.66 Kbytes malloced 2929
% 2.41/2.66
% 2.41/2.66 ----------- times (seconds) -----------
% 2.41/2.66 user CPU time 0.51 (0 hr, 0 min, 0 sec)
% 2.41/2.66 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.41/2.66 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.41/2.66
% 2.41/2.66 That finishes the proof of the theorem.
% 2.41/2.66
% 2.41/2.66 Process 5305 finished Wed Jul 27 06:34:37 2022
% 2.41/2.67 Otter interrupted
% 2.41/2.67 PROOF FOUND
%------------------------------------------------------------------------------