TSTP Solution File: RNG095+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG095+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 13:12:16 EDT 2022
% Result : Theorem 56.77s 56.96s
% Output : Refutation 56.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 5 unt; 0 nHn; 9 RR)
% Number of literals : 14 ( 3 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(65,axiom,
( ~ aElement0(A)
| aElementOf0(dollar_f13(A),xI) ),
file('RNG095+2.p',unknown),
[] ).
cnf(66,axiom,
( ~ aElement0(A)
| aElementOf0(dollar_f12(A),xJ) ),
file('RNG095+2.p',unknown),
[] ).
cnf(67,axiom,
( ~ aElement0(A)
| sdtpldt0(dollar_f13(A),dollar_f12(A)) = A ),
file('RNG095+2.p',unknown),
[] ).
cnf(69,axiom,
( ~ aElementOf0(A,xI)
| ~ aElementOf0(B,xJ)
| sdtpldt0(A,B) != sz10 ),
file('RNG095+2.p',unknown),
[] ).
cnf(148,axiom,
aElement0(sz10),
file('RNG095+2.p',unknown),
[] ).
cnf(279,plain,
sdtpldt0(dollar_f13(sz10),dollar_f12(sz10)) = sz10,
inference(hyper,[status(thm)],[148,67]),
[iquote('hyper,148,67')] ).
cnf(281,plain,
aElementOf0(dollar_f12(sz10),xJ),
inference(hyper,[status(thm)],[148,66]),
[iquote('hyper,148,66')] ).
cnf(282,plain,
aElementOf0(dollar_f13(sz10),xI),
inference(hyper,[status(thm)],[148,65]),
[iquote('hyper,148,65')] ).
cnf(2014,plain,
$false,
inference(hyper,[status(thm)],[279,69,282,281]),
[iquote('hyper,279,69,282,281')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG095+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 02:06:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.94/2.15 ----- Otter 3.3f, August 2004 -----
% 1.94/2.15 The process was started by sandbox on n021.cluster.edu,
% 1.94/2.15 Wed Jul 27 02:06:08 2022
% 1.94/2.15 The command was "./otter". The process ID is 25222.
% 1.94/2.15
% 1.94/2.15 set(prolog_style_variables).
% 1.94/2.15 set(auto).
% 1.94/2.15 dependent: set(auto1).
% 1.94/2.15 dependent: set(process_input).
% 1.94/2.15 dependent: clear(print_kept).
% 1.94/2.15 dependent: clear(print_new_demod).
% 1.94/2.15 dependent: clear(print_back_demod).
% 1.94/2.15 dependent: clear(print_back_sub).
% 1.94/2.15 dependent: set(control_memory).
% 1.94/2.15 dependent: assign(max_mem, 12000).
% 1.94/2.15 dependent: assign(pick_given_ratio, 4).
% 1.94/2.15 dependent: assign(stats_level, 1).
% 1.94/2.15 dependent: assign(max_seconds, 10800).
% 1.94/2.15 clear(print_given).
% 1.94/2.15
% 1.94/2.15 formula_list(usable).
% 1.94/2.15 all A (A=A).
% 1.94/2.15 all W0 (aElement0(W0)->$T).
% 1.94/2.15 aElement0(sz00).
% 1.94/2.15 aElement0(sz10).
% 1.94/2.15 all W0 (aElement0(W0)->aElement0(smndt0(W0))).
% 1.94/2.15 all W0 W1 (aElement0(W0)&aElement0(W1)->aElement0(sdtpldt0(W0,W1))).
% 1.94/2.15 all W0 W1 (aElement0(W0)&aElement0(W1)->aElement0(sdtasdt0(W0,W1))).
% 1.94/2.15 all W0 W1 (aElement0(W0)&aElement0(W1)->sdtpldt0(W0,W1)=sdtpldt0(W1,W0)).
% 1.94/2.15 all W0 W1 W2 (aElement0(W0)&aElement0(W1)&aElement0(W2)->sdtpldt0(sdtpldt0(W0,W1),W2)=sdtpldt0(W0,sdtpldt0(W1,W2))).
% 1.94/2.15 all W0 (aElement0(W0)->sdtpldt0(W0,sz00)=W0&W0=sdtpldt0(sz00,W0)).
% 1.94/2.15 all W0 (aElement0(W0)->sdtpldt0(W0,smndt0(W0))=sz00&sz00=sdtpldt0(smndt0(W0),W0)).
% 1.94/2.15 all W0 W1 (aElement0(W0)&aElement0(W1)->sdtasdt0(W0,W1)=sdtasdt0(W1,W0)).
% 1.94/2.15 all W0 W1 W2 (aElement0(W0)&aElement0(W1)&aElement0(W2)->sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2))).
% 1.94/2.15 all W0 (aElement0(W0)->sdtasdt0(W0,sz10)=W0&W0=sdtasdt0(sz10,W0)).
% 1.94/2.15 all W0 W1 W2 (aElement0(W0)&aElement0(W1)&aElement0(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))).
% 1.94/2.15 all W0 (aElement0(W0)->sdtasdt0(smndt0(sz10),W0)=smndt0(W0)&smndt0(W0)=sdtasdt0(W0,smndt0(sz10))).
% 1.94/2.15 all W0 (aElement0(W0)->sdtasdt0(W0,sz00)=sz00&sz00=sdtasdt0(sz00,W0)).
% 1.94/2.15 all W0 W1 (aElement0(W0)&aElement0(W1)-> (sdtasdt0(W0,W1)=sz00->W0=sz00|W1=sz00)).
% 1.94/2.15 sz10!=sz00.
% 1.94/2.15 all W0 (aSet0(W0)->$T).
% 1.94/2.15 all W0 (aSet0(W0)-> (all W1 (aElementOf0(W1,W0)->aElement0(W1)))).
% 1.94/2.15 all W0 W1 (aSet0(W0)&aSet0(W1)-> ((all W2 (aElementOf0(W2,W0)->aElementOf0(W2,W1)))& (all W2 (aElementOf0(W2,W1)->aElementOf0(W2,W0)))->W0=W1)).
% 1.94/2.15 all W0 W1 (aSet0(W0)&aSet0(W1)-> (all W2 (W2=sdtpldt1(W0,W1)<->aSet0(W2)& (all W3 (aElementOf0(W3,W2)<-> (exists W4 W5 (aElementOf0(W4,W0)&aElementOf0(W5,W1)&sdtpldt0(W4,W5)=W3))))))).
% 1.94/2.15 all W0 W1 (aSet0(W0)&aSet0(W1)-> (all W2 (W2=sdtasasdt0(W0,W1)<->aSet0(W2)& (all W3 (aElementOf0(W3,W2)<->aElementOf0(W3,W0)&aElementOf0(W3,W1)))))).
% 1.94/2.15 all W0 (aIdeal0(W0)<->aSet0(W0)& (all W1 (aElementOf0(W1,W0)-> (all W2 (aElementOf0(W2,W0)->aElementOf0(sdtpldt0(W1,W2),W0)))& (all W2 (aElement0(W2)->aElementOf0(sdtasdt0(W2,W1),W0)))))).
% 1.94/2.15 all W0 W1 (aIdeal0(W0)&aIdeal0(W1)->aIdeal0(sdtpldt1(W0,W1))).
% 1.94/2.15 all W0 W1 (aIdeal0(W0)&aIdeal0(W1)->aIdeal0(sdtasasdt0(W0,W1))).
% 1.94/2.15 all W0 W1 W2 (aElement0(W0)&aElement0(W1)&aIdeal0(W2)-> (sdte_qdtlpzmzozddtrp0(W0,W1,W2)<->aElementOf0(sdtpldt0(W0,smndt0(W1)),W2))).
% 1.94/2.15 aSet0(xI).
% 1.94/2.15 all W0 (aElementOf0(W0,xI)-> (all W1 (aElementOf0(W1,xI)->aElementOf0(sdtpldt0(W0,W1),xI)))& (all W1 (aElement0(W1)->aElementOf0(sdtasdt0(W1,W0),xI)))).
% 1.94/2.15 aIdeal0(xI).
% 1.94/2.15 aSet0(xJ).
% 1.94/2.15 all W0 (aElementOf0(W0,xJ)-> (all W1 (aElementOf0(W1,xJ)->aElementOf0(sdtpldt0(W0,W1),xJ)))& (all W1 (aElement0(W1)->aElementOf0(sdtasdt0(W1,W0),xJ)))).
% 1.94/2.15 aIdeal0(xJ).
% 1.94/2.15 all W0 (aElement0(W0)-> (exists W1 W2 (aElementOf0(W1,xI)&aElementOf0(W2,xJ)&sdtpldt0(W1,W2)=W0))&aElementOf0(W0,sdtpldt1(xI,xJ))).
% 1.94/2.15 aElement0(xx).
% 1.94/2.15 aElement0(xy).
% 1.94/2.15 -(exists W0 W1 (aElementOf0(W0,xI)&aElementOf0(W1,xJ)&sdtpldt0(W0,W1)=sz10)).
% 1.94/2.15 end_of_list.
% 1.94/2.15
% 1.94/2.15 -------> usable clausifies to:
% 1.94/2.15
% 1.94/2.15 list(usable).
% 1.94/2.15 0 [] A=A.
% 1.94/2.15 0 [] -aElement0(W0)|$T.
% 1.94/2.15 0 [] aElement0(sz00).
% 1.94/2.15 0 [] aElement0(sz10).
% 1.94/2.15 0 [] -aElement0(W0)|aElement0(smndt0(W0)).
% 1.94/2.15 0 [] -aElement0(W0)| -aElement0(W1)|aElement0(sdtpldt0(W0,W1)).
% 1.94/2.15 0 [] -aElement0(W0)| -aElement0(W1)|aElement0(sdtasdt0(W0,W1)).
% 1.94/2.15 0 [] -aElement0(W0)| -aElement0(W1)|sdtpldt0(W0,W1)=sdtpldt0(W1,W0).
% 1.94/2.15 0 [] -aElement0(W0)| -aElement0(W1)| -aElement0(W2)|sdtpldt0(sdtpldt0(W0,W1),W2)=sdtpldt0(W0,sdtpldt0(W1,W2)).
% 1.94/2.15 0 [] -aElement0(W0)|sdtpldt0(W0,sz00)=W0.
% 1.94/2.15 0 [] -aElement0(W0)|W0=sdtpldt0(sz00,W0).
% 1.94/2.15 0 [] -aElement0(W0)|sdtpldt0(W0,smndt0(W0))=sz00.
% 1.94/2.15 0 [] -aElement0(W0)|sz00=sdtpldt0(smndt0(W0),W0).
% 1.94/2.15 0 [] -aElement0(W0)| -aElement0(W1)|sdtasdt0(W0,W1)=sdtasdt0(W1,W0).
% 1.94/2.15 0 [] -aElement0(W0)| -aElement0(W1)| -aElement0(W2)|sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2)).
% 1.94/2.15 0 [] -aElement0(W0)|sdtasdt0(W0,sz10)=W0.
% 1.94/2.15 0 [] -aElement0(W0)|W0=sdtasdt0(sz10,W0).
% 1.94/2.15 0 [] -aElement0(W0)| -aElement0(W1)| -aElement0(W2)|sdtasdt0(W0,sdtpldt0(W1,W2))=sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)).
% 1.94/2.15 0 [] -aElement0(W0)| -aElement0(W1)| -aElement0(W2)|sdtasdt0(sdtpldt0(W1,W2),W0)=sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)).
% 1.94/2.15 0 [] -aElement0(W0)|sdtasdt0(smndt0(sz10),W0)=smndt0(W0).
% 1.94/2.15 0 [] -aElement0(W0)|smndt0(W0)=sdtasdt0(W0,smndt0(sz10)).
% 1.94/2.15 0 [] -aElement0(W0)|sdtasdt0(W0,sz00)=sz00.
% 1.94/2.15 0 [] -aElement0(W0)|sz00=sdtasdt0(sz00,W0).
% 1.94/2.15 0 [] -aElement0(W0)| -aElement0(W1)|sdtasdt0(W0,W1)!=sz00|W0=sz00|W1=sz00.
% 1.94/2.15 0 [] sz10!=sz00.
% 1.94/2.15 0 [] -aSet0(W0)|$T.
% 1.94/2.15 0 [] -aSet0(W0)| -aElementOf0(W1,W0)|aElement0(W1).
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|aElementOf0($f1(W0,W1),W0)|aElementOf0($f2(W0,W1),W1)|W0=W1.
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|aElementOf0($f1(W0,W1),W0)| -aElementOf0($f2(W0,W1),W0)|W0=W1.
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)| -aElementOf0($f1(W0,W1),W1)|aElementOf0($f2(W0,W1),W1)|W0=W1.
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)| -aElementOf0($f1(W0,W1),W1)| -aElementOf0($f2(W0,W1),W0)|W0=W1.
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2!=sdtpldt1(W0,W1)|aSet0(W2).
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2!=sdtpldt1(W0,W1)| -aElementOf0(W3,W2)|aElementOf0($f4(W0,W1,W2,W3),W0).
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2!=sdtpldt1(W0,W1)| -aElementOf0(W3,W2)|aElementOf0($f3(W0,W1,W2,W3),W1).
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2!=sdtpldt1(W0,W1)| -aElementOf0(W3,W2)|sdtpldt0($f4(W0,W1,W2,W3),$f3(W0,W1,W2,W3))=W3.
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2!=sdtpldt1(W0,W1)|aElementOf0(W3,W2)| -aElementOf0(W4,W0)| -aElementOf0(W5,W1)|sdtpldt0(W4,W5)!=W3.
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2=sdtpldt1(W0,W1)| -aSet0(W2)|aElementOf0($f7(W0,W1,W2),W2)|aElementOf0($f6(W0,W1,W2),W0).
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2=sdtpldt1(W0,W1)| -aSet0(W2)|aElementOf0($f7(W0,W1,W2),W2)|aElementOf0($f5(W0,W1,W2),W1).
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2=sdtpldt1(W0,W1)| -aSet0(W2)|aElementOf0($f7(W0,W1,W2),W2)|sdtpldt0($f6(W0,W1,W2),$f5(W0,W1,W2))=$f7(W0,W1,W2).
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2=sdtpldt1(W0,W1)| -aSet0(W2)| -aElementOf0($f7(W0,W1,W2),W2)| -aElementOf0(X1,W0)| -aElementOf0(X2,W1)|sdtpldt0(X1,X2)!=$f7(W0,W1,W2).
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2!=sdtasasdt0(W0,W1)|aSet0(W2).
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2!=sdtasasdt0(W0,W1)| -aElementOf0(W3,W2)|aElementOf0(W3,W0).
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2!=sdtasasdt0(W0,W1)| -aElementOf0(W3,W2)|aElementOf0(W3,W1).
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2!=sdtasasdt0(W0,W1)|aElementOf0(W3,W2)| -aElementOf0(W3,W0)| -aElementOf0(W3,W1).
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2=sdtasasdt0(W0,W1)| -aSet0(W2)|aElementOf0($f8(W0,W1,W2),W2)|aElementOf0($f8(W0,W1,W2),W0).
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2=sdtasasdt0(W0,W1)| -aSet0(W2)|aElementOf0($f8(W0,W1,W2),W2)|aElementOf0($f8(W0,W1,W2),W1).
% 1.94/2.15 0 [] -aSet0(W0)| -aSet0(W1)|W2=sdtasasdt0(W0,W1)| -aSet0(W2)| -aElementOf0($f8(W0,W1,W2),W2)| -aElementOf0($f8(W0,W1,W2),W0)| -aElementOf0($f8(W0,W1,W2),W1).
% 1.94/2.15 0 [] -aIdeal0(W0)|aSet0(W0).
% 1.94/2.15 0 [] -aIdeal0(W0)| -aElementOf0(W1,W0)| -aElementOf0(W2,W0)|aElementOf0(sdtpldt0(W1,W2),W0).
% 1.94/2.15 0 [] -aIdeal0(W0)| -aElementOf0(W1,W0)| -aElement0(X3)|aElementOf0(sdtasdt0(X3,W1),W0).
% 1.94/2.15 0 [] aIdeal0(W0)| -aSet0(W0)|aElementOf0($f11(W0),W0).
% 1.94/2.15 0 [] aIdeal0(W0)| -aSet0(W0)|aElementOf0($f9(W0),W0)|aElement0($f10(W0)).
% 1.94/2.15 0 [] aIdeal0(W0)| -aSet0(W0)|aElementOf0($f9(W0),W0)| -aElementOf0(sdtasdt0($f10(W0),$f11(W0)),W0).
% 1.94/2.15 0 [] aIdeal0(W0)| -aSet0(W0)| -aElementOf0(sdtpldt0($f11(W0),$f9(W0)),W0)|aElement0($f10(W0)).
% 1.94/2.15 0 [] aIdeal0(W0)| -aSet0(W0)| -aElementOf0(sdtpldt0($f11(W0),$f9(W0)),W0)| -aElementOf0(sdtasdt0($f10(W0),$f11(W0)),W0).
% 1.94/2.15 0 [] -aIdeal0(W0)| -aIdeal0(W1)|aIdeal0(sdtpldt1(W0,W1)).
% 1.94/2.15 0 [] -aIdeal0(W0)| -aIdeal0(W1)|aIdeal0(sdtasasdt0(W0,W1)).
% 1.94/2.15 0 [] -aElement0(W0)| -aElement0(W1)| -aIdeal0(W2)| -sdte_qdtlpzmzozddtrp0(W0,W1,W2)|aElementOf0(sdtpldt0(W0,smndt0(W1)),W2).
% 1.94/2.16 0 [] -aElement0(W0)| -aElement0(W1)| -aIdeal0(W2)|sdte_qdtlpzmzozddtrp0(W0,W1,W2)| -aElementOf0(sdtpldt0(W0,smndt0(W1)),W2).
% 1.94/2.16 0 [] aSet0(xI).
% 1.94/2.16 0 [] -aElementOf0(W0,xI)| -aElementOf0(W1,xI)|aElementOf0(sdtpldt0(W0,W1),xI).
% 1.94/2.16 0 [] -aElementOf0(W0,xI)| -aElement0(X4)|aElementOf0(sdtasdt0(X4,W0),xI).
% 1.94/2.16 0 [] aIdeal0(xI).
% 1.94/2.16 0 [] aSet0(xJ).
% 1.94/2.16 0 [] -aElementOf0(W0,xJ)| -aElementOf0(W1,xJ)|aElementOf0(sdtpldt0(W0,W1),xJ).
% 1.94/2.16 0 [] -aElementOf0(W0,xJ)| -aElement0(X5)|aElementOf0(sdtasdt0(X5,W0),xJ).
% 1.94/2.16 0 [] aIdeal0(xJ).
% 1.94/2.16 0 [] -aElement0(W0)|aElementOf0($f13(W0),xI).
% 1.94/2.16 0 [] -aElement0(W0)|aElementOf0($f12(W0),xJ).
% 1.94/2.16 0 [] -aElement0(W0)|sdtpldt0($f13(W0),$f12(W0))=W0.
% 1.94/2.16 0 [] -aElement0(W0)|aElementOf0(W0,sdtpldt1(xI,xJ)).
% 1.94/2.16 0 [] aElement0(xx).
% 1.94/2.16 0 [] aElement0(xy).
% 1.94/2.16 0 [] -aElementOf0(W0,xI)| -aElementOf0(W1,xJ)|sdtpldt0(W0,W1)!=sz10.
% 1.94/2.16 end_of_list.
% 1.94/2.16
% 1.94/2.16 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 1.94/2.16
% 1.94/2.16 This ia a non-Horn set with equality. The strategy will be
% 1.94/2.16 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.94/2.16 deletion, with positive clauses in sos and nonpositive
% 1.94/2.16 clauses in usable.
% 1.94/2.16
% 1.94/2.16 dependent: set(knuth_bendix).
% 1.94/2.16 dependent: set(anl_eq).
% 1.94/2.16 dependent: set(para_from).
% 1.94/2.16 dependent: set(para_into).
% 1.94/2.16 dependent: clear(para_from_right).
% 1.94/2.16 dependent: clear(para_into_right).
% 1.94/2.16 dependent: set(para_from_vars).
% 1.94/2.16 dependent: set(eq_units_both_ways).
% 1.94/2.16 dependent: set(dynamic_demod_all).
% 1.94/2.16 dependent: set(dynamic_demod).
% 1.94/2.16 dependent: set(order_eq).
% 1.94/2.16 dependent: set(back_demod).
% 1.94/2.16 dependent: set(lrpo).
% 1.94/2.16 dependent: set(hyper_res).
% 1.94/2.16 dependent: set(unit_deletion).
% 1.94/2.16 dependent: set(factor).
% 1.94/2.16
% 1.94/2.16 ------------> process usable:
% 1.94/2.16 ** KEPT (pick-wt=5): 1 [] -aElement0(A)|aElement0(smndt0(A)).
% 1.94/2.16 ** KEPT (pick-wt=8): 2 [] -aElement0(A)| -aElement0(B)|aElement0(sdtpldt0(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=8): 3 [] -aElement0(A)| -aElement0(B)|aElement0(sdtasdt0(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=11): 4 [] -aElement0(A)| -aElement0(B)|sdtpldt0(A,B)=sdtpldt0(B,A).
% 1.94/2.16 ** KEPT (pick-wt=17): 5 [] -aElement0(A)| -aElement0(B)| -aElement0(C)|sdtpldt0(sdtpldt0(A,B),C)=sdtpldt0(A,sdtpldt0(B,C)).
% 1.94/2.16 ** KEPT (pick-wt=7): 6 [] -aElement0(A)|sdtpldt0(A,sz00)=A.
% 1.94/2.16 ** KEPT (pick-wt=7): 8 [copy,7,flip.2] -aElement0(A)|sdtpldt0(sz00,A)=A.
% 1.94/2.16 ** KEPT (pick-wt=8): 9 [] -aElement0(A)|sdtpldt0(A,smndt0(A))=sz00.
% 1.94/2.16 ** KEPT (pick-wt=8): 11 [copy,10,flip.2] -aElement0(A)|sdtpldt0(smndt0(A),A)=sz00.
% 1.94/2.16 ** KEPT (pick-wt=11): 12 [] -aElement0(A)| -aElement0(B)|sdtasdt0(A,B)=sdtasdt0(B,A).
% 1.94/2.16 ** KEPT (pick-wt=17): 13 [] -aElement0(A)| -aElement0(B)| -aElement0(C)|sdtasdt0(sdtasdt0(A,B),C)=sdtasdt0(A,sdtasdt0(B,C)).
% 1.94/2.16 ** KEPT (pick-wt=7): 14 [] -aElement0(A)|sdtasdt0(A,sz10)=A.
% 1.94/2.16 ** KEPT (pick-wt=7): 16 [copy,15,flip.2] -aElement0(A)|sdtasdt0(sz10,A)=A.
% 1.94/2.16 ** KEPT (pick-wt=19): 18 [copy,17,flip.4] -aElement0(A)| -aElement0(B)| -aElement0(C)|sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C))=sdtasdt0(A,sdtpldt0(B,C)).
% 1.94/2.16 ** KEPT (pick-wt=19): 20 [copy,19,flip.4] -aElement0(A)| -aElement0(B)| -aElement0(C)|sdtpldt0(sdtasdt0(B,A),sdtasdt0(C,A))=sdtasdt0(sdtpldt0(B,C),A).
% 1.94/2.16 ** KEPT (pick-wt=9): 21 [] -aElement0(A)|sdtasdt0(smndt0(sz10),A)=smndt0(A).
% 1.94/2.16 ** KEPT (pick-wt=9): 22 [] -aElement0(A)|smndt0(A)=sdtasdt0(A,smndt0(sz10)).
% 1.94/2.16 ** KEPT (pick-wt=7): 23 [] -aElement0(A)|sdtasdt0(A,sz00)=sz00.
% 1.94/2.16 ** KEPT (pick-wt=7): 25 [copy,24,flip.2] -aElement0(A)|sdtasdt0(sz00,A)=sz00.
% 1.94/2.16 ** KEPT (pick-wt=15): 26 [] -aElement0(A)| -aElement0(B)|sdtasdt0(A,B)!=sz00|A=sz00|B=sz00.
% 1.94/2.16 ** KEPT (pick-wt=3): 27 [] sz10!=sz00.
% 1.94/2.16 ** KEPT (pick-wt=7): 28 [] -aSet0(A)| -aElementOf0(B,A)|aElement0(B).
% 1.94/2.16 ** KEPT (pick-wt=17): 29 [] -aSet0(A)| -aSet0(B)|aElementOf0($f1(A,B),A)|aElementOf0($f2(A,B),B)|A=B.
% 1.94/2.16 ** KEPT (pick-wt=17): 30 [] -aSet0(A)| -aSet0(B)|aElementOf0($f1(A,B),A)| -aElementOf0($f2(A,B),A)|A=B.
% 1.94/2.16 ** KEPT (pick-wt=17): 31 [] -aSet0(A)| -aSet0(B)| -aElementOf0($f1(A,B),B)|aElementOf0($f2(A,B),B)|A=B.
% 1.94/2.16 ** KEPT (pick-wt=17): 32 [] -aSet0(A)| -aSet0(B)| -aElementOf0($f1(A,B),B)| -aElementOf0($f2(A,B),A)|A=B.
% 1.94/2.16 ** KEPT (pick-wt=11): 33 [] -aSet0(A)| -aSet0(B)|C!=sdtpldt1(A,B)|aSet0(C).
% 1.94/2.16 ** KEPT (pick-wt=19): 34 [] -aSet0(A)| -aSet0(B)|C!=sdtpldt1(A,B)| -aElementOf0(D,C)|aElementOf0($f4(A,B,C,D),A).
% 1.94/2.16 ** KEPT (pick-wt=19): 35 [] -aSet0(A)| -aSet0(B)|C!=sdtpldt1(A,B)| -aElementOf0(D,C)|aElementOf0($f3(A,B,C,D),B).
% 1.94/2.16 ** KEPT (pick-wt=25): 36 [] -aSet0(A)| -aSet0(B)|C!=sdtpldt1(A,B)| -aElementOf0(D,C)|sdtpldt0($f4(A,B,C,D),$f3(A,B,C,D))=D.
% 1.94/2.16 ** KEPT (pick-wt=23): 37 [] -aSet0(A)| -aSet0(B)|C!=sdtpldt1(A,B)|aElementOf0(D,C)| -aElementOf0(E,A)| -aElementOf0(F,B)|sdtpldt0(E,F)!=D.
% 1.94/2.16 ** KEPT (pick-wt=23): 38 [] -aSet0(A)| -aSet0(B)|C=sdtpldt1(A,B)| -aSet0(C)|aElementOf0($f7(A,B,C),C)|aElementOf0($f6(A,B,C),A).
% 1.94/2.16 ** KEPT (pick-wt=23): 39 [] -aSet0(A)| -aSet0(B)|C=sdtpldt1(A,B)| -aSet0(C)|aElementOf0($f7(A,B,C),C)|aElementOf0($f5(A,B,C),B).
% 1.94/2.16 ** KEPT (pick-wt=31): 40 [] -aSet0(A)| -aSet0(B)|C=sdtpldt1(A,B)| -aSet0(C)|aElementOf0($f7(A,B,C),C)|sdtpldt0($f6(A,B,C),$f5(A,B,C))=$f7(A,B,C).
% 1.94/2.16 ** KEPT (pick-wt=31): 41 [] -aSet0(A)| -aSet0(B)|C=sdtpldt1(A,B)| -aSet0(C)| -aElementOf0($f7(A,B,C),C)| -aElementOf0(D,A)| -aElementOf0(E,B)|sdtpldt0(D,E)!=$f7(A,B,C).
% 1.94/2.16 ** KEPT (pick-wt=11): 42 [] -aSet0(A)| -aSet0(B)|C!=sdtasasdt0(A,B)|aSet0(C).
% 1.94/2.16 ** KEPT (pick-wt=15): 43 [] -aSet0(A)| -aSet0(B)|C!=sdtasasdt0(A,B)| -aElementOf0(D,C)|aElementOf0(D,A).
% 1.94/2.16 ** KEPT (pick-wt=15): 44 [] -aSet0(A)| -aSet0(B)|C!=sdtasasdt0(A,B)| -aElementOf0(D,C)|aElementOf0(D,B).
% 1.94/2.16 ** KEPT (pick-wt=18): 45 [] -aSet0(A)| -aSet0(B)|C!=sdtasasdt0(A,B)|aElementOf0(D,C)| -aElementOf0(D,A)| -aElementOf0(D,B).
% 1.94/2.16 ** KEPT (pick-wt=23): 46 [] -aSet0(A)| -aSet0(B)|C=sdtasasdt0(A,B)| -aSet0(C)|aElementOf0($f8(A,B,C),C)|aElementOf0($f8(A,B,C),A).
% 1.94/2.16 ** KEPT (pick-wt=23): 47 [] -aSet0(A)| -aSet0(B)|C=sdtasasdt0(A,B)| -aSet0(C)|aElementOf0($f8(A,B,C),C)|aElementOf0($f8(A,B,C),B).
% 1.94/2.16 ** KEPT (pick-wt=29): 48 [] -aSet0(A)| -aSet0(B)|C=sdtasasdt0(A,B)| -aSet0(C)| -aElementOf0($f8(A,B,C),C)| -aElementOf0($f8(A,B,C),A)| -aElementOf0($f8(A,B,C),B).
% 1.94/2.16 ** KEPT (pick-wt=4): 49 [] -aIdeal0(A)|aSet0(A).
% 1.94/2.16 ** KEPT (pick-wt=13): 50 [] -aIdeal0(A)| -aElementOf0(B,A)| -aElementOf0(C,A)|aElementOf0(sdtpldt0(B,C),A).
% 1.94/2.16 ** KEPT (pick-wt=12): 51 [] -aIdeal0(A)| -aElementOf0(B,A)| -aElement0(C)|aElementOf0(sdtasdt0(C,B),A).
% 1.94/2.16 ** KEPT (pick-wt=8): 52 [] aIdeal0(A)| -aSet0(A)|aElementOf0($f11(A),A).
% 1.94/2.16 ** KEPT (pick-wt=11): 53 [] aIdeal0(A)| -aSet0(A)|aElementOf0($f9(A),A)|aElement0($f10(A)).
% 1.94/2.16 ** KEPT (pick-wt=15): 54 [] aIdeal0(A)| -aSet0(A)|aElementOf0($f9(A),A)| -aElementOf0(sdtasdt0($f10(A),$f11(A)),A).
% 1.94/2.16 ** KEPT (pick-wt=14): 55 [] aIdeal0(A)| -aSet0(A)| -aElementOf0(sdtpldt0($f11(A),$f9(A)),A)|aElement0($f10(A)).
% 1.94/2.16 ** KEPT (pick-wt=18): 56 [] aIdeal0(A)| -aSet0(A)| -aElementOf0(sdtpldt0($f11(A),$f9(A)),A)| -aElementOf0(sdtasdt0($f10(A),$f11(A)),A).
% 1.94/2.16 ** KEPT (pick-wt=8): 57 [] -aIdeal0(A)| -aIdeal0(B)|aIdeal0(sdtpldt1(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=8): 58 [] -aIdeal0(A)| -aIdeal0(B)|aIdeal0(sdtasasdt0(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=16): 59 [] -aElement0(A)| -aElement0(B)| -aIdeal0(C)| -sdte_qdtlpzmzozddtrp0(A,B,C)|aElementOf0(sdtpldt0(A,smndt0(B)),C).
% 1.94/2.16 ** KEPT (pick-wt=16): 60 [] -aElement0(A)| -aElement0(B)| -aIdeal0(C)|sdte_qdtlpzmzozddtrp0(A,B,C)| -aElementOf0(sdtpldt0(A,smndt0(B)),C).
% 1.94/2.16 ** KEPT (pick-wt=11): 61 [] -aElementOf0(A,xI)| -aElementOf0(B,xI)|aElementOf0(sdtpldt0(A,B),xI).
% 1.94/2.16 ** KEPT (pick-wt=10): 62 [] -aElementOf0(A,xI)| -aElement0(B)|aElementOf0(sdtasdt0(B,A),xI).
% 1.94/2.16 ** KEPT (pick-wt=11): 63 [] -aElementOf0(A,xJ)| -aElementOf0(B,xJ)|aElementOf0(sdtpldt0(A,B),xJ).
% 1.94/2.16 ** KEPT (pick-wt=10): 64 [] -aElementOf0(A,xJ)| -aElement0(B)|aElementOf0(sdtasdt0(B,A),xJ).
% 1.94/2.16 ** KEPT (pick-wt=6): 65 [] -aElement0(A)|aElementOf0($f13(A),xI).
% 1.94/2.16 ** KEPT (pick-wt=6): 66 [] -aElement0(A)|aElementOf0($f12(A),xJ).
% 1.94/2.16 ** KEPT (pick-wt=9): 67 [] -aElement0(A)|sdtpldt0($f13(A),$f12(A))=A.
% 1.94/2.16 ** KEPT (pick-wt=7): 68 [] -aElement0(A)|aElementOf0(A,sdtpldt1(xI,xJ)).
% 1.94/2.16 ** KEPT (pick-wt=11): 69 [] -aElementOf0(A,xI)| -aElementOf0(B,xJ)|sdtpldt0(A,B)!=sz10.
% 1.94/2.16 119 back subsumes 118.
% 1.94/2.16
% 1.94/2.16 ------------> process sos:
% 1.94/2.16 ** KEPT (pick-wt=3): 146 [] A=A.
% 1.94/2.16 ** KEPT (pick-wt=2): 147 [] aElement0(sz00).
% 1.94/2.16 ** KEPT (pick-wt=2): 148 [] aElement0(sz10).
% 1.94/2.16 ** KEPT (pick-wt=2): 149 [] aSet0(xI).
% 1.94/2.16 ** KEPT (pick-wt=2): 150 [] aIdeal0(xI).
% 1.94/2.16 ** KEPT (pick-wt=2): 151 [] aSet0(xJ).
% 1.94/2.16 ** KEPT (pick-wt=2): 152 [] aIdeal0(xJ).
% 56.77/56.96 ** KEPT (pick-wt=2): 153 [] aElement0(xx).
% 56.77/56.96 ** KEPT (pick-wt=2): 154 [] aElement0(xy).
% 56.77/56.96 Following clause subsumed by 146 during input processing: 0 [copy,146,flip.1] A=A.
% 56.77/56.96 146 back subsumes 90.
% 56.77/56.96 146 back subsumes 89.
% 56.77/56.96 146 back subsumes 88.
% 56.77/56.96 146 back subsumes 87.
% 56.77/56.96 146 back subsumes 76.
% 56.77/56.96 146 back subsumes 72.
% 56.77/56.96
% 56.77/56.96 ======= end of input processing =======
% 56.77/56.96
% 56.77/56.96 =========== start of search ===========
% 56.77/56.96
% 56.77/56.96
% 56.77/56.96 Resetting weight limit to 5.
% 56.77/56.96
% 56.77/56.96
% 56.77/56.96 Resetting weight limit to 5.
% 56.77/56.96
% 56.77/56.96 sos_size=651
% 56.77/56.96
% 56.77/56.96 -- HEY sandbox, WE HAVE A PROOF!! --
% 56.77/56.96
% 56.77/56.96 -----> EMPTY CLAUSE at 54.80 sec ----> 2014 [hyper,279,69,282,281] $F.
% 56.77/56.96
% 56.77/56.96 Length of proof is 3. Level of proof is 1.
% 56.77/56.96
% 56.77/56.96 ---------------- PROOF ----------------
% 56.77/56.96 % SZS status Theorem
% 56.77/56.96 % SZS output start Refutation
% See solution above
% 56.77/56.96 ------------ end of proof -------------
% 56.77/56.96
% 56.77/56.96
% 56.77/56.96 Search stopped by max_proofs option.
% 56.77/56.96
% 56.77/56.96
% 56.77/56.96 Search stopped by max_proofs option.
% 56.77/56.96
% 56.77/56.96 ============ end of search ============
% 56.77/56.96
% 56.77/56.96 -------------- statistics -------------
% 56.77/56.96 clauses given 266
% 56.77/56.96 clauses generated 14324015
% 56.77/56.96 clauses kept 1438
% 56.77/56.96 clauses forward subsumed 2749
% 56.77/56.96 clauses back subsumed 12
% 56.77/56.96 Kbytes malloced 5859
% 56.77/56.96
% 56.77/56.96 ----------- times (seconds) -----------
% 56.77/56.96 user CPU time 54.80 (0 hr, 0 min, 54 sec)
% 56.77/56.96 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 56.77/56.96 wall-clock time 56 (0 hr, 0 min, 56 sec)
% 56.77/56.96
% 56.77/56.96 That finishes the proof of the theorem.
% 56.77/56.96
% 56.77/56.96 Process 25222 finished Wed Jul 27 02:07:04 2022
% 56.77/56.96 Otter interrupted
% 56.77/56.96 PROOF FOUND
%------------------------------------------------------------------------------