%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM538+2 : 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 13:08:45 EDT 2022
% Result : Theorem 5.79s 6.01s
% Output : Refutation 5.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of clauses : 16 ( 11 unt; 1 nHn; 15 RR)
% Number of literals : 28 ( 6 equ; 13 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ aSet0(A)
| ~ aElementOf0(B,A)
| aElement0(B) ),
file('NUM538+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ aSet0(A)
| ~ aElementOf0(B,A)
| sdtpldt0(sdtmndt0(A,B),B) = A ),
file('NUM538+2.p',unknown),
[] ).
cnf(38,axiom,
( ~ aElement0(A)
| ~ aSet0(B)
| ~ isFinite0(B)
| isFinite0(sdtmndt0(B,A)) ),
file('NUM538+2.p',unknown),
[] ).
cnf(62,axiom,
( ~ aSet0(A)
| ~ isFinite0(A)
| ~ aElement0(B)
| aElementOf0(B,A)
| sbrdtbr0(sdtpldt0(A,B)) = szszuzczcdt0(sbrdtbr0(A)) ),
file('NUM538+2.p',unknown),
[] ).
cnf(65,axiom,
( ~ aElementOf0(A,sdtmndt0(xS,xx))
| A != xx ),
file('NUM538+2.p',unknown),
[] ).
cnf(67,axiom,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
file('NUM538+2.p',unknown),
[] ).
cnf(81,axiom,
A = A,
file('NUM538+2.p',unknown),
[] ).
cnf(86,axiom,
aSet0(xS),
file('NUM538+2.p',unknown),
[] ).
cnf(87,axiom,
isFinite0(xS),
file('NUM538+2.p',unknown),
[] ).
cnf(88,axiom,
aElementOf0(xx,xS),
file('NUM538+2.p',unknown),
[] ).
cnf(89,axiom,
aSet0(sdtmndt0(xS,xx)),
file('NUM538+2.p',unknown),
[] ).
cnf(351,plain,
sdtpldt0(sdtmndt0(xS,xx),xx) = xS,
inference(hyper,[status(thm)],[88,33,86]),
[iquote('hyper,88,33,86')] ).
cnf(352,plain,
aElement0(xx),
inference(hyper,[status(thm)],[88,1,86]),
[iquote('hyper,88,1,86')] ).
cnf(519,plain,
isFinite0(sdtmndt0(xS,xx)),
inference(hyper,[status(thm)],[352,38,86,87]),
[iquote('hyper,352,38,86,87')] ).
cnf(1800,plain,
aElementOf0(xx,sdtmndt0(xS,xx)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[519,62,89,352]),351]),67]),
[iquote('hyper,519,62,89,352,demod,351,unit_del,67')] ).
cnf(1903,plain,
$false,
inference(hyper,[status(thm)],[1800,65,81]),
[iquote('hyper,1800,65,81')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM538+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 10:00:44 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.98/2.19 ----- Otter 3.3f, August 2004 -----
% 1.98/2.19 The process was started by sandbox2 on n029.cluster.edu,
% 1.98/2.19 Wed Jul 27 10:00:44 2022
% 1.98/2.19 The command was "./otter". The process ID is 32125.
% 1.98/2.19
% 1.98/2.19 set(prolog_style_variables).
% 1.98/2.19 set(auto).
% 1.98/2.19 dependent: set(auto1).
% 1.98/2.19 dependent: set(process_input).
% 1.98/2.19 dependent: clear(print_kept).
% 1.98/2.19 dependent: clear(print_new_demod).
% 1.98/2.19 dependent: clear(print_back_demod).
% 1.98/2.19 dependent: clear(print_back_sub).
% 1.98/2.19 dependent: set(control_memory).
% 1.98/2.19 dependent: assign(max_mem, 12000).
% 1.98/2.19 dependent: assign(pick_given_ratio, 4).
% 1.98/2.19 dependent: assign(stats_level, 1).
% 1.98/2.19 dependent: assign(max_seconds, 10800).
% 1.98/2.19 clear(print_given).
% 1.98/2.19
% 1.98/2.19 formula_list(usable).
% 1.98/2.19 all A (A=A).
% 1.98/2.19 all W0 (aSet0(W0)->$T).
% 1.98/2.19 all W0 (aElement0(W0)->$T).
% 1.98/2.19 all W0 (aSet0(W0)-> (all W1 (aElementOf0(W1,W0)->aElement0(W1)))).
% 1.98/2.19 all W0 (aSet0(W0)-> (isFinite0(W0)->$T)).
% 1.98/2.19 all W0 (W0=slcrc0<->aSet0(W0)& -(exists W1 aElementOf0(W1,W0))).
% 1.98/2.19 isFinite0(slcrc0).
% 1.98/2.19 all W0 (aSet0(W0)-> (isCountable0(W0)->$T)).
% 1.98/2.19 all W0 (aSet0(W0)&isCountable0(W0)-> -isFinite0(W0)).
% 1.98/2.19 all W0 (aSet0(W0)&isCountable0(W0)->W0!=slcrc0).
% 1.98/2.19 all W0 (aSet0(W0)-> (all W1 (aSubsetOf0(W1,W0)<->aSet0(W1)& (all W2 (aElementOf0(W2,W1)->aElementOf0(W2,W0)))))).
% 1.98/2.19 all W0 (aSet0(W0)&isFinite0(W0)-> (all W1 (aSubsetOf0(W1,W0)->isFinite0(W1)))).
% 1.98/2.19 all W0 (aSet0(W0)->aSubsetOf0(W0,W0)).
% 1.98/2.19 all W0 W1 (aSet0(W0)&aSet0(W1)-> (aSubsetOf0(W0,W1)&aSubsetOf0(W1,W0)->W0=W1)).
% 1.98/2.19 all W0 W1 W2 (aSet0(W0)&aSet0(W1)&aSet0(W2)-> (aSubsetOf0(W0,W1)&aSubsetOf0(W1,W2)->aSubsetOf0(W0,W2))).
% 1.98/2.19 all W0 W1 (aSet0(W0)&aElement0(W1)-> (all W2 (W2=sdtpldt0(W0,W1)<->aSet0(W2)& (all W3 (aElementOf0(W3,W2)<->aElement0(W3)& (aElementOf0(W3,W0)|W3=W1)))))).
% 1.98/2.19 all W0 W1 (aSet0(W0)&aElement0(W1)-> (all W2 (W2=sdtmndt0(W0,W1)<->aSet0(W2)& (all W3 (aElementOf0(W3,W2)<->aElement0(W3)&aElementOf0(W3,W0)&W3!=W1))))).
% 1.98/2.19 all W0 (aSet0(W0)-> (all W1 (aElementOf0(W1,W0)->sdtpldt0(sdtmndt0(W0,W1),W1)=W0))).
% 1.98/2.19 all W0 W1 (aElement0(W0)&aSet0(W1)-> (-aElementOf0(W0,W1)->sdtmndt0(sdtpldt0(W1,W0),W0)=W1)).
% 1.98/2.19 all W0 (aElement0(W0)-> (all W1 (aSet0(W1)&isCountable0(W1)->isCountable0(sdtpldt0(W1,W0))))).
% 1.98/2.19 all W0 (aElement0(W0)-> (all W1 (aSet0(W1)&isCountable0(W1)->isCountable0(sdtmndt0(W1,W0))))).
% 1.98/2.19 all W0 (aElement0(W0)-> (all W1 (aSet0(W1)&isFinite0(W1)->isFinite0(sdtpldt0(W1,W0))))).
% 1.98/2.19 all W0 (aElement0(W0)-> (all W1 (aSet0(W1)&isFinite0(W1)->isFinite0(sdtmndt0(W1,W0))))).
% 1.98/2.19 aSet0(szNzAzT0).
% 1.98/2.19 isCountable0(szNzAzT0).
% 1.98/2.19 aElementOf0(sz00,szNzAzT0).
% 1.98/2.19 all W0 (aElementOf0(W0,szNzAzT0)->aElementOf0(szszuzczcdt0(W0),szNzAzT0)&szszuzczcdt0(W0)!=sz00).
% 1.98/2.19 all W0 W1 (aElementOf0(W0,szNzAzT0)&aElementOf0(W1,szNzAzT0)-> (szszuzczcdt0(W0)=szszuzczcdt0(W1)->W0=W1)).
% 1.98/2.19 all W0 (aElementOf0(W0,szNzAzT0)->W0=sz00| (exists W1 (aElementOf0(W1,szNzAzT0)&W0=szszuzczcdt0(W1)))).
% 1.98/2.19 all W0 (aElementOf0(W0,szNzAzT0)->W0!=szszuzczcdt0(W0)).
% 1.98/2.19 all W0 W1 (aElementOf0(W0,szNzAzT0)&aElementOf0(W1,szNzAzT0)-> (sdtlse_qdt0(W0,W1)->$T)).
% 1.98/2.19 all W0 (aElementOf0(W0,szNzAzT0)->sdtlse_qdt0(sz00,W0)).
% 1.98/2.19 all W0 (aElementOf0(W0,szNzAzT0)-> -sdtlse_qdt0(szszuzczcdt0(W0),sz00)).
% 1.98/2.19 all W0 W1 (aElementOf0(W0,szNzAzT0)&aElementOf0(W1,szNzAzT0)-> (sdtlse_qdt0(W0,W1)<->sdtlse_qdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)))).
% 1.98/2.19 all W0 (aElementOf0(W0,szNzAzT0)->sdtlse_qdt0(W0,szszuzczcdt0(W0))).
% 1.98/2.19 all W0 (aElementOf0(W0,szNzAzT0)->sdtlse_qdt0(W0,W0)).
% 1.98/2.19 all W0 W1 (aElementOf0(W0,szNzAzT0)&aElementOf0(W1,szNzAzT0)-> (sdtlse_qdt0(W0,W1)&sdtlse_qdt0(W1,W0)->W0=W1)).
% 1.98/2.19 all W0 W1 W2 (aElementOf0(W0,szNzAzT0)&aElementOf0(W1,szNzAzT0)&aElementOf0(W2,szNzAzT0)-> (sdtlse_qdt0(W0,W1)&sdtlse_qdt0(W1,W2)->sdtlse_qdt0(W0,W2))).
% 1.98/2.19 all W0 W1 (aElementOf0(W0,szNzAzT0)&aElementOf0(W1,szNzAzT0)->sdtlse_qdt0(W0,W1)|sdtlse_qdt0(szszuzczcdt0(W1),W0)).
% 1.98/2.19 all W0 W1 (aElementOf0(W0,szNzAzT0)&aElementOf0(W1,szNzAzT0)-> (iLess0(W0,W1)->$T)).
% 1.98/2.19 all W0 (aElementOf0(W0,szNzAzT0)->iLess0(W0,szszuzczcdt0(W0))).
% 1.98/2.19 all W0 (aSet0(W0)->aElement0(sbrdtbr0(W0))).
% 1.98/2.19 all W0 (aSet0(W0)-> (aElementOf0(sbrdtbr0(W0),szNzAzT0)<->isFinite0(W0))).
% 1.98/2.19 all W0 (aSet0(W0)-> (sbrdtbr0(W0)=sz00<->W0=slcrc0)).
% 1.98/2.19 all W0 (aSet0(W0)&isFinite0(W0)-> (all W1 (aElement0(W1)-> (-aElementOf0(W1,W0)->sbrdtbr0(sdtpldt0(W0,W1))=szszuzczcdt0(sbrdtbr0(W0)))))).
% 1.98/2.19 aSet0(xS).
% 1.98/2.19 isFinite0(xS).
% 1.98/2.19 aElementOf0(xx,xS).
% 1.98/2.19 -(aSet0(sdtmndt0(xS,xx))& (all W0 (aElementOf0(W0,sdtmndt0(xS,xx))<->aElement0(W0)&aElementOf0(W0,xS)&W0!=xx))->szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx)))=sbrdtbr0(xS)).
% 1.98/2.19 end_of_list.
% 1.98/2.19
% 1.98/2.19 -------> usable clausifies to:
% 1.98/2.19
% 1.98/2.19 list(usable).
% 1.98/2.19 0 [] A=A.
% 1.98/2.19 0 [] -aSet0(W0)|$T.
% 1.98/2.19 0 [] -aElement0(W0)|$T.
% 1.98/2.19 0 [] -aSet0(W0)| -aElementOf0(W1,W0)|aElement0(W1).
% 1.98/2.19 0 [] -aSet0(W0)| -isFinite0(W0)|$T.
% 1.98/2.19 0 [] W0!=slcrc0|aSet0(W0).
% 1.98/2.19 0 [] W0!=slcrc0| -aElementOf0(W1,W0).
% 1.98/2.19 0 [] W0=slcrc0| -aSet0(W0)|aElementOf0($f1(W0),W0).
% 1.98/2.19 0 [] isFinite0(slcrc0).
% 1.98/2.19 0 [] -aSet0(W0)| -isCountable0(W0)|$T.
% 1.98/2.19 0 [] -aSet0(W0)| -isCountable0(W0)| -isFinite0(W0).
% 1.98/2.19 0 [] -aSet0(W0)| -isCountable0(W0)|W0!=slcrc0.
% 1.98/2.19 0 [] -aSet0(W0)| -aSubsetOf0(W1,W0)|aSet0(W1).
% 1.98/2.19 0 [] -aSet0(W0)| -aSubsetOf0(W1,W0)| -aElementOf0(W2,W1)|aElementOf0(W2,W0).
% 1.98/2.19 0 [] -aSet0(W0)|aSubsetOf0(W1,W0)| -aSet0(W1)|aElementOf0($f2(W0,W1),W1).
% 1.98/2.19 0 [] -aSet0(W0)|aSubsetOf0(W1,W0)| -aSet0(W1)| -aElementOf0($f2(W0,W1),W0).
% 1.98/2.19 0 [] -aSet0(W0)| -isFinite0(W0)| -aSubsetOf0(W1,W0)|isFinite0(W1).
% 1.98/2.19 0 [] -aSet0(W0)|aSubsetOf0(W0,W0).
% 1.98/2.19 0 [] -aSet0(W0)| -aSet0(W1)| -aSubsetOf0(W0,W1)| -aSubsetOf0(W1,W0)|W0=W1.
% 1.98/2.19 0 [] -aSet0(W0)| -aSet0(W1)| -aSet0(W2)| -aSubsetOf0(W0,W1)| -aSubsetOf0(W1,W2)|aSubsetOf0(W0,W2).
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2!=sdtpldt0(W0,W1)|aSet0(W2).
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2!=sdtpldt0(W0,W1)| -aElementOf0(W3,W2)|aElement0(W3).
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2!=sdtpldt0(W0,W1)| -aElementOf0(W3,W2)|aElementOf0(W3,W0)|W3=W1.
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2!=sdtpldt0(W0,W1)|aElementOf0(W3,W2)| -aElement0(W3)| -aElementOf0(W3,W0).
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2!=sdtpldt0(W0,W1)|aElementOf0(W3,W2)| -aElement0(W3)|W3!=W1.
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2=sdtpldt0(W0,W1)| -aSet0(W2)|aElementOf0($f3(W0,W1,W2),W2)|aElement0($f3(W0,W1,W2)).
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2=sdtpldt0(W0,W1)| -aSet0(W2)|aElementOf0($f3(W0,W1,W2),W2)|aElementOf0($f3(W0,W1,W2),W0)|$f3(W0,W1,W2)=W1.
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2=sdtpldt0(W0,W1)| -aSet0(W2)| -aElementOf0($f3(W0,W1,W2),W2)| -aElement0($f3(W0,W1,W2))| -aElementOf0($f3(W0,W1,W2),W0).
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2=sdtpldt0(W0,W1)| -aSet0(W2)| -aElementOf0($f3(W0,W1,W2),W2)| -aElement0($f3(W0,W1,W2))|$f3(W0,W1,W2)!=W1.
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2!=sdtmndt0(W0,W1)|aSet0(W2).
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2!=sdtmndt0(W0,W1)| -aElementOf0(W3,W2)|aElement0(W3).
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2!=sdtmndt0(W0,W1)| -aElementOf0(W3,W2)|aElementOf0(W3,W0).
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2!=sdtmndt0(W0,W1)| -aElementOf0(W3,W2)|W3!=W1.
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2!=sdtmndt0(W0,W1)|aElementOf0(W3,W2)| -aElement0(W3)| -aElementOf0(W3,W0)|W3=W1.
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2=sdtmndt0(W0,W1)| -aSet0(W2)|aElementOf0($f4(W0,W1,W2),W2)|aElement0($f4(W0,W1,W2)).
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2=sdtmndt0(W0,W1)| -aSet0(W2)|aElementOf0($f4(W0,W1,W2),W2)|aElementOf0($f4(W0,W1,W2),W0).
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2=sdtmndt0(W0,W1)| -aSet0(W2)|aElementOf0($f4(W0,W1,W2),W2)|$f4(W0,W1,W2)!=W1.
% 1.98/2.19 0 [] -aSet0(W0)| -aElement0(W1)|W2=sdtmndt0(W0,W1)| -aSet0(W2)| -aElementOf0($f4(W0,W1,W2),W2)| -aElement0($f4(W0,W1,W2))| -aElementOf0($f4(W0,W1,W2),W0)|$f4(W0,W1,W2)=W1.
% 1.98/2.19 0 [] -aSet0(W0)| -aElementOf0(W1,W0)|sdtpldt0(sdtmndt0(W0,W1),W1)=W0.
% 1.98/2.19 0 [] -aElement0(W0)| -aSet0(W1)|aElementOf0(W0,W1)|sdtmndt0(sdtpldt0(W1,W0),W0)=W1.
% 1.98/2.19 0 [] -aElement0(W0)| -aSet0(W1)| -isCountable0(W1)|isCountable0(sdtpldt0(W1,W0)).
% 1.98/2.19 0 [] -aElement0(W0)| -aSet0(W1)| -isCountable0(W1)|isCountable0(sdtmndt0(W1,W0)).
% 1.98/2.19 0 [] -aElement0(W0)| -aSet0(W1)| -isFinite0(W1)|isFinite0(sdtpldt0(W1,W0)).
% 1.98/2.19 0 [] -aElement0(W0)| -aSet0(W1)| -isFinite0(W1)|isFinite0(sdtmndt0(W1,W0)).
% 1.98/2.19 0 [] aSet0(szNzAzT0).
% 1.98/2.19 0 [] isCountable0(szNzAzT0).
% 1.98/2.19 0 [] aElementOf0(sz00,szNzAzT0).
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)|aElementOf0(szszuzczcdt0(W0),szNzAzT0).
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)|szszuzczcdt0(W0)!=sz00.
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)| -aElementOf0(W1,szNzAzT0)|szszuzczcdt0(W0)!=szszuzczcdt0(W1)|W0=W1.
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)|W0=sz00|aElementOf0($f5(W0),szNzAzT0).
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)|W0=sz00|W0=szszuzczcdt0($f5(W0)).
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)|W0!=szszuzczcdt0(W0).
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)| -aElementOf0(W1,szNzAzT0)| -sdtlse_qdt0(W0,W1)|$T.
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)|sdtlse_qdt0(sz00,W0).
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)| -sdtlse_qdt0(szszuzczcdt0(W0),sz00).
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)| -aElementOf0(W1,szNzAzT0)| -sdtlse_qdt0(W0,W1)|sdtlse_qdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)).
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)| -aElementOf0(W1,szNzAzT0)|sdtlse_qdt0(W0,W1)| -sdtlse_qdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)).
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)|sdtlse_qdt0(W0,szszuzczcdt0(W0)).
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)|sdtlse_qdt0(W0,W0).
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)| -aElementOf0(W1,szNzAzT0)| -sdtlse_qdt0(W0,W1)| -sdtlse_qdt0(W1,W0)|W0=W1.
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)| -aElementOf0(W1,szNzAzT0)| -aElementOf0(W2,szNzAzT0)| -sdtlse_qdt0(W0,W1)| -sdtlse_qdt0(W1,W2)|sdtlse_qdt0(W0,W2).
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)| -aElementOf0(W1,szNzAzT0)|sdtlse_qdt0(W0,W1)|sdtlse_qdt0(szszuzczcdt0(W1),W0).
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)| -aElementOf0(W1,szNzAzT0)| -iLess0(W0,W1)|$T.
% 1.98/2.19 0 [] -aElementOf0(W0,szNzAzT0)|iLess0(W0,szszuzczcdt0(W0)).
% 1.98/2.19 0 [] -aSet0(W0)|aElement0(sbrdtbr0(W0)).
% 1.98/2.19 0 [] -aSet0(W0)| -aElementOf0(sbrdtbr0(W0),szNzAzT0)|isFinite0(W0).
% 1.98/2.19 0 [] -aSet0(W0)|aElementOf0(sbrdtbr0(W0),szNzAzT0)| -isFinite0(W0).
% 1.98/2.19 0 [] -aSet0(W0)|sbrdtbr0(W0)!=sz00|W0=slcrc0.
% 1.98/2.19 0 [] -aSet0(W0)|sbrdtbr0(W0)=sz00|W0!=slcrc0.
% 1.98/2.19 0 [] -aSet0(W0)| -isFinite0(W0)| -aElement0(W1)|aElementOf0(W1,W0)|sbrdtbr0(sdtpldt0(W0,W1))=szszuzczcdt0(sbrdtbr0(W0)).
% 1.98/2.19 0 [] aSet0(xS).
% 1.98/2.19 0 [] isFinite0(xS).
% 1.98/2.19 0 [] aElementOf0(xx,xS).
% 1.98/2.19 0 [] aSet0(sdtmndt0(xS,xx)).
% 1.98/2.19 0 [] -aElementOf0(W0,sdtmndt0(xS,xx))|aElement0(W0).
% 1.98/2.19 0 [] -aElementOf0(W0,sdtmndt0(xS,xx))|aElementOf0(W0,xS).
% 1.98/2.19 0 [] -aElementOf0(W0,sdtmndt0(xS,xx))|W0!=xx.
% 1.98/2.19 0 [] aElementOf0(W0,sdtmndt0(xS,xx))| -aElement0(W0)| -aElementOf0(W0,xS)|W0=xx.
% 1.98/2.19 0 [] szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx)))!=sbrdtbr0(xS).
% 1.98/2.19 end_of_list.
% 1.98/2.19
% 1.98/2.19 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 1.98/2.19
% 1.98/2.19 This ia a non-Horn set with equality. The strategy will be
% 1.98/2.19 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.98/2.19 deletion, with positive clauses in sos and nonpositive
% 1.98/2.19 clauses in usable.
% 1.98/2.19
% 1.98/2.19 dependent: set(knuth_bendix).
% 1.98/2.19 dependent: set(anl_eq).
% 1.98/2.19 dependent: set(para_from).
% 1.98/2.19 dependent: set(para_into).
% 1.98/2.19 dependent: clear(para_from_right).
% 1.98/2.19 dependent: clear(para_into_right).
% 1.98/2.19 dependent: set(para_from_vars).
% 1.98/2.19 dependent: set(eq_units_both_ways).
% 1.98/2.19 dependent: set(dynamic_demod_all).
% 1.98/2.19 dependent: set(dynamic_demod).
% 1.98/2.19 dependent: set(order_eq).
% 1.98/2.19 dependent: set(back_demod).
% 1.98/2.19 dependent: set(lrpo).
% 1.98/2.19 dependent: set(hyper_res).
% 1.98/2.19 dependent: set(unit_deletion).
% 1.98/2.19 dependent: set(factor).
% 1.98/2.19
% 1.98/2.19 ------------> process usable:
% 1.98/2.19 ** KEPT (pick-wt=7): 1 [] -aSet0(A)| -aElementOf0(B,A)|aElement0(B).
% 1.98/2.19 ** KEPT (pick-wt=5): 2 [] A!=slcrc0|aSet0(A).
% 1.98/2.19 ** KEPT (pick-wt=6): 3 [] A!=slcrc0| -aElementOf0(B,A).
% 1.98/2.19 ** KEPT (pick-wt=9): 4 [] A=slcrc0| -aSet0(A)|aElementOf0($f1(A),A).
% 1.98/2.19 ** KEPT (pick-wt=6): 5 [] -aSet0(A)| -isCountable0(A)| -isFinite0(A).
% 1.98/2.19 ** KEPT (pick-wt=7): 6 [] -aSet0(A)| -isCountable0(A)|A!=slcrc0.
% 1.98/2.19 ** KEPT (pick-wt=7): 7 [] -aSet0(A)| -aSubsetOf0(B,A)|aSet0(B).
% 1.98/2.19 ** KEPT (pick-wt=11): 8 [] -aSet0(A)| -aSubsetOf0(B,A)| -aElementOf0(C,B)|aElementOf0(C,A).
% 1.98/2.19 ** KEPT (pick-wt=12): 9 [] -aSet0(A)|aSubsetOf0(B,A)| -aSet0(B)|aElementOf0($f2(A,B),B).
% 1.98/2.19 ** KEPT (pick-wt=12): 10 [] -aSet0(A)|aSubsetOf0(B,A)| -aSet0(B)| -aElementOf0($f2(A,B),A).
% 1.98/2.19 ** KEPT (pick-wt=9): 11 [] -aSet0(A)| -isFinite0(A)| -aSubsetOf0(B,A)|isFinite0(B).
% 1.98/2.19 ** KEPT (pick-wt=5): 12 [] -aSet0(A)|aSubsetOf0(A,A).
% 1.98/2.19 ** KEPT (pick-wt=13): 13 [] -aSet0(A)| -aSet0(B)| -aSubsetOf0(A,B)| -aSubsetOf0(B,A)|A=B.
% 1.98/2.19 ** KEPT (pick-wt=15): 14 [] -aSet0(A)| -aSet0(B)| -aSet0(C)| -aSubsetOf0(A,B)| -aSubsetOf0(B,C)|aSubsetOf0(A,C).
% 1.98/2.19 ** KEPT (pick-wt=11): 15 [] -aSet0(A)| -aElement0(B)|C!=sdtpldt0(A,B)|aSet0(C).
% 1.98/2.19 ** KEPT (pick-wt=14): 16 [] -aSet0(A)| -aElement0(B)|C!=sdtpldt0(A,B)| -aElementOf0(D,C)|aElement0(D).
% 1.98/2.19 ** KEPT (pick-wt=18): 17 [] -aSet0(A)| -aElement0(B)|C!=sdtpldt0(A,B)| -aElementOf0(D,C)|aElementOf0(D,A)|D=B.
% 1.98/2.19 ** KEPT (pick-wt=17): 18 [] -aSet0(A)| -aElement0(B)|C!=sdtpldt0(A,B)|aElementOf0(D,C)| -aElement0(D)| -aElementOf0(D,A).
% 1.98/2.19 ** KEPT (pick-wt=17): 19 [] -aSet0(A)| -aElement0(B)|C!=sdtpldt0(A,B)|aElementOf0(D,C)| -aElement0(D)|D!=B.
% 1.98/2.19 ** KEPT (pick-wt=22): 20 [] -aSet0(A)| -aElement0(B)|C=sdtpldt0(A,B)| -aSet0(C)|aElementOf0($f3(A,B,C),C)|aElement0($f3(A,B,C)).
% 1.98/2.19 ** KEPT (pick-wt=29): 21 [] -aSet0(A)| -aElement0(B)|C=sdtpldt0(A,B)| -aSet0(C)|aElementOf0($f3(A,B,C),C)|aElementOf0($f3(A,B,C),A)|$f3(A,B,C)=B.
% 1.98/2.19 ** KEPT (pick-wt=28): 22 [] -aSet0(A)| -aElement0(B)|C=sdtpldt0(A,B)| -aSet0(C)| -aElementOf0($f3(A,B,C),C)| -aElement0($f3(A,B,C))| -aElementOf0($f3(A,B,C),A).
% 1.98/2.19 ** KEPT (pick-wt=28): 23 [] -aSet0(A)| -aElement0(B)|C=sdtpldt0(A,B)| -aSet0(C)| -aElementOf0($f3(A,B,C),C)| -aElement0($f3(A,B,C))|$f3(A,B,C)!=B.
% 1.98/2.19 ** KEPT (pick-wt=11): 24 [] -aSet0(A)| -aElement0(B)|C!=sdtmndt0(A,B)|aSet0(C).
% 1.98/2.19 ** KEPT (pick-wt=14): 25 [] -aSet0(A)| -aElement0(B)|C!=sdtmndt0(A,B)| -aElementOf0(D,C)|aElement0(D).
% 1.98/2.19 ** KEPT (pick-wt=15): 26 [] -aSet0(A)| -aElement0(B)|C!=sdtmndt0(A,B)| -aElementOf0(D,C)|aElementOf0(D,A).
% 1.98/2.19 ** KEPT (pick-wt=15): 27 [] -aSet0(A)| -aElement0(B)|C!=sdtmndt0(A,B)| -aElementOf0(D,C)|D!=B.
% 1.98/2.19 ** KEPT (pick-wt=20): 28 [] -aSet0(A)| -aElement0(B)|C!=sdtmndt0(A,B)|aElementOf0(D,C)| -aElement0(D)| -aElementOf0(D,A)|D=B.
% 1.98/2.19 ** KEPT (pick-wt=22): 29 [] -aSet0(A)| -aElement0(B)|C=sdtmndt0(A,B)| -aSet0(C)|aElementOf0($f4(A,B,C),C)|aElement0($f4(A,B,C)).
% 1.98/2.19 ** KEPT (pick-wt=23): 30 [] -aSet0(A)| -aElement0(B)|C=sdtmndt0(A,B)| -aSet0(C)|aElementOf0($f4(A,B,C),C)|aElementOf0($f4(A,B,C),A).
% 1.98/2.19 ** KEPT (pick-wt=23): 31 [] -aSet0(A)| -aElement0(B)|C=sdtmndt0(A,B)| -aSet0(C)|aElementOf0($f4(A,B,C),C)|$f4(A,B,C)!=B.
% 1.98/2.19 ** KEPT (pick-wt=34): 32 [] -aSet0(A)| -aElement0(B)|C=sdtmndt0(A,B)| -aSet0(C)| -aElementOf0($f4(A,B,C),C)| -aElement0($f4(A,B,C))| -aElementOf0($f4(A,B,C),A)|$f4(A,B,C)=B.
% 1.98/2.19 ** KEPT (pick-wt=12): 33 [] -aSet0(A)| -aElementOf0(B,A)|sdtpldt0(sdtmndt0(A,B),B)=A.
% 1.98/2.19 ** KEPT (pick-wt=14): 34 [] -aElement0(A)| -aSet0(B)|aElementOf0(A,B)|sdtmndt0(sdtpldt0(B,A),A)=B.
% 1.98/2.19 ** KEPT (pick-wt=10): 35 [] -aElement0(A)| -aSet0(B)| -isCountable0(B)|isCountable0(sdtpldt0(B,A)).
% 1.98/2.19 ** KEPT (pick-wt=10): 36 [] -aElement0(A)| -aSet0(B)| -isCountable0(B)|isCountable0(sdtmndt0(B,A)).
% 1.98/2.19 ** KEPT (pick-wt=10): 37 [] -aElement0(A)| -aSet0(B)| -isFinite0(B)|isFinite0(sdtpldt0(B,A)).
% 1.98/2.19 ** KEPT (pick-wt=10): 38 [] -aElement0(A)| -aSet0(B)| -isFinite0(B)|isFinite0(sdtmndt0(B,A)).
% 1.98/2.19 ** KEPT (pick-wt=7): 39 [] -aElementOf0(A,szNzAzT0)|aElementOf0(szszuzczcdt0(A),szNzAzT0).
% 1.98/2.19 ** KEPT (pick-wt=7): 40 [] -aElementOf0(A,szNzAzT0)|szszuzczcdt0(A)!=sz00.
% 1.98/2.19 ** KEPT (pick-wt=14): 41 [] -aElementOf0(A,szNzAzT0)| -aElementOf0(B,szNzAzT0)|szszuzczcdt0(A)!=szszuzczcdt0(B)|A=B.
% 1.98/2.19 ** KEPT (pick-wt=10): 42 [] -aElementOf0(A,szNzAzT0)|A=sz00|aElementOf0($f5(A),szNzAzT0).
% 1.98/2.19 ** KEPT (pick-wt=11): 44 [copy,43,flip.3] -aElementOf0(A,szNzAzT0)|A=sz00|szszuzczcdt0($f5(A))=A.
% 1.98/2.19 ** KEPT (pick-wt=7): 46 [copy,45,flip.2] -aElementOf0(A,szNzAzT0)|szszuzczcdt0(A)!=A.
% 1.98/2.19 ** KEPT (pick-wt=6): 47 [] -aElementOf0(A,szNzAzT0)|sdtlse_qdt0(sz00,A).
% 1.98/2.19 ** KEPT (pick-wt=7): 48 [] -aElementOf0(A,szNzAzT0)| -sdtlse_qdt0(szszuzczcdt0(A),sz00).
% 1.98/2.19 ** KEPT (pick-wt=14): 49 [] -aElementOf0(A,szNzAzT0)| -aElementOf0(B,szNzAzT0)| -sdtlse_qdt0(A,B)|sdtlse_qdt0(szszuzczcdt0(A),szszuzczcdt0(B)).
% 1.98/2.19 ** KEPT (pick-wt=14): 50 [] -aElementOf0(A,szNzAzT0)| -aElementOf0(B,szNzAzT0)|sdtlse_qdt0(A,B)| -sdtlse_qdt0(szszuzczcdt0(A),szszuzczcdt0(B)).
% 1.98/2.19 ** KEPT (pick-wt=7): 51 [] -aElementOf0(A,szNzAzT0)|sdtlse_qdt0(A,szszuzczcdt0(A)).
% 1.98/2.19 ** KEPT (pick-wt=6): 52 [] -aElementOf0(A,szNzAzT0)|sdtlse_qdt0(A,A).
% 1.98/2.19 ** KEPT (pick-wt=15): 53 [] -aElementOf0(A,szNzAzT0)| -aElementOf0(B,szNzAzT0)| -sdtlse_qdt0(A,B)| -sdtlse_qdt0(B,A)|A=B.
% 1.98/2.19 ** KEPT (pick-wt=18): 54 [] -aElementOf0(A,szNzAzT0)| -aElementOf0(B,szNzAzT0)| -aElementOf0(C,szNzAzT0)| -sdtlse_qdt0(A,B)| -sdtlse_qdt0(B,C)|sdtlse_qdt0(A,C).
% 1.98/2.19 ** KEPT (pick-wt=13): 55 [] -aElementOf0(A,szNzAzT0)| -aElementOf0(B,szNzAzT0)|sdtlse_qdt0(A,B)|sdtlse_qdt0(szszuzczcdt0(B),A).
% 1.98/2.19 ** KEPT (pick-wt=7): 56 [] -aElementOf0(A,szNzAzT0)|iLess0(A,szszuzczcdt0(A)).
% 5.79/6.01 ** KEPT (pick-wt=5): 57 [] -aSet0(A)|aElement0(sbrdtbr0(A)).
% 5.79/6.01 ** KEPT (pick-wt=8): 58 [] -aSet0(A)| -aElementOf0(sbrdtbr0(A),szNzAzT0)|isFinite0(A).
% 5.79/6.01 ** KEPT (pick-wt=8): 59 [] -aSet0(A)|aElementOf0(sbrdtbr0(A),szNzAzT0)| -isFinite0(A).
% 5.79/6.01 ** KEPT (pick-wt=9): 60 [] -aSet0(A)|sbrdtbr0(A)!=sz00|A=slcrc0.
% 5.79/6.01 ** KEPT (pick-wt=9): 61 [] -aSet0(A)|sbrdtbr0(A)=sz00|A!=slcrc0.
% 5.79/6.01 ** KEPT (pick-wt=17): 62 [] -aSet0(A)| -isFinite0(A)| -aElement0(B)|aElementOf0(B,A)|sbrdtbr0(sdtpldt0(A,B))=szszuzczcdt0(sbrdtbr0(A)).
% 5.79/6.01 ** KEPT (pick-wt=7): 63 [] -aElementOf0(A,sdtmndt0(xS,xx))|aElement0(A).
% 5.79/6.01 ** KEPT (pick-wt=8): 64 [] -aElementOf0(A,sdtmndt0(xS,xx))|aElementOf0(A,xS).
% 5.79/6.01 ** KEPT (pick-wt=8): 65 [] -aElementOf0(A,sdtmndt0(xS,xx))|A!=xx.
% 5.79/6.01 ** KEPT (pick-wt=13): 66 [] aElementOf0(A,sdtmndt0(xS,xx))| -aElement0(A)| -aElementOf0(A,xS)|A=xx.
% 5.79/6.01 ** KEPT (pick-wt=8): 67 [] szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx)))!=sbrdtbr0(xS).
% 5.79/6.01 76 back subsumes 75.
% 5.79/6.01
% 5.79/6.01 ------------> process sos:
% 5.79/6.01 ** KEPT (pick-wt=3): 81 [] A=A.
% 5.79/6.01 ** KEPT (pick-wt=2): 82 [] isFinite0(slcrc0).
% 5.79/6.01 ** KEPT (pick-wt=2): 83 [] aSet0(szNzAzT0).
% 5.79/6.01 ** KEPT (pick-wt=2): 84 [] isCountable0(szNzAzT0).
% 5.79/6.01 ** KEPT (pick-wt=3): 85 [] aElementOf0(sz00,szNzAzT0).
% 5.79/6.01 ** KEPT (pick-wt=2): 86 [] aSet0(xS).
% 5.79/6.01 ** KEPT (pick-wt=2): 87 [] isFinite0(xS).
% 5.79/6.01 ** KEPT (pick-wt=3): 88 [] aElementOf0(xx,xS).
% 5.79/6.01 ** KEPT (pick-wt=4): 89 [] aSet0(sdtmndt0(xS,xx)).
% 5.79/6.01 Following clause subsumed by 81 during input processing: 0 [copy,81,flip.1] A=A.
% 5.79/6.01 81 back subsumes 80.
% 5.79/6.01 81 back subsumes 78.
% 5.79/6.01 81 back subsumes 74.
% 5.79/6.01 81 back subsumes 68.
% 5.79/6.01
% 5.79/6.01 ======= end of input processing =======
% 5.79/6.01
% 5.79/6.01 =========== start of search ===========
% 5.79/6.01
% 5.79/6.01
% 5.79/6.01 Resetting weight limit to 7.
% 5.79/6.01
% 5.79/6.01
% 5.79/6.01 Resetting weight limit to 7.
% 5.79/6.01
% 5.79/6.01 sos_size=1472
% 5.79/6.01
% 5.79/6.01
% 5.79/6.01 Resetting weight limit to 6.
% 5.79/6.01
% 5.79/6.01
% 5.79/6.01 Resetting weight limit to 6.
% 5.79/6.01
% 5.79/6.01 sos_size=1629
% 5.79/6.01
% 5.79/6.01 -------- PROOF --------
% 5.79/6.01
% 5.79/6.01 -----> EMPTY CLAUSE at 3.83 sec ----> 1903 [hyper,1800,65,81] $F.
% 5.79/6.01
% 5.79/6.01 Length of proof is 4. Level of proof is 3.
% 5.79/6.01
% 5.79/6.01 ---------------- PROOF ----------------
% 5.79/6.01 % SZS status Theorem
% 5.79/6.01 % SZS output start Refutation
% See solution above
% 5.79/6.01 ------------ end of proof -------------
% 5.79/6.01
% 5.79/6.01
% 5.79/6.01 Search stopped by max_proofs option.
% 5.79/6.01
% 5.79/6.01
% 5.79/6.01 Search stopped by max_proofs option.
% 5.79/6.01
% 5.79/6.01 ============ end of search ============
% 5.79/6.01
% 5.79/6.01 -------------- statistics -------------
% 5.79/6.01 clauses given 129
% 5.79/6.01 clauses generated 80980
% 5.79/6.01 clauses kept 1896
% 5.79/6.01 clauses forward subsumed 963
% 5.79/6.01 clauses back subsumed 47
% 5.79/6.01 Kbytes malloced 4882
% 5.79/6.01
% 5.79/6.01 ----------- times (seconds) -----------
% 5.79/6.01 user CPU time 3.83 (0 hr, 0 min, 3 sec)
% 5.79/6.01 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 5.79/6.01 wall-clock time 6 (0 hr, 0 min, 6 sec)
% 5.79/6.01
% 5.79/6.01 That finishes the proof of the theorem.
% 5.79/6.01
% 5.79/6.01 Process 32125 finished Wed Jul 27 10:00:50 2022
% 5.79/6.01 Otter interrupted
% 5.79/6.01 PROOF FOUND
%------------------------------------------------------------------------------